^^^^'
JO .^.iJto.
THE,
ELEMENTS
o
OF
G
I C.
iJQUR BOOKS.
BOQK I.
Ci" the original of our ideas,
rheir various divisions, and
the manner in which ihey
contribute to the increase of
knov.ledofe ; with a philo-
so
progress,
man language.
BOOK II.
Of the grounds of human judg-
ment, the doctrine cf pro-
positions, their use in reason-
ing, and division into self-
evident and demonstrable.
phical account c£ the rise,
and nature of hu-
BOOK III.
Of reasoning and demonstra-
tion, with their application
to the investigation of knowl-
edge, and the conamon af-
fairs of life.
BOOK IV.
Of the methods of invention,
and science, where the sev-
eral degrees cf evidence are
examined, the notion of cer-
tainty is fixed and stated,
and the parts cf knowrledge
in vrhich it may be attained.
DESIGNED PARTICULARLY FOR
T'oimg Gentlemen at* the Un'roersity ; ^
AND TO PREPARE THE V/AY TO THE STUDY OF
PHILOSOPHY AXD THE MATHEMATICS.
5y WILLIA?^I DUXXAN,
Professor of Philcsophy in MarishaL College, Aberdeen.
Dcctrina sed vim promovet insitam ;
Rectiqiie cultus pectora roborant Hop...
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I
TO THE
RIGHT HONORABLE
STEPHEN POYNTZ, Esc^,
SIR,
If I take this opportunity of publishin^^ to the world
the esteem I have for a character to wiiich learning
is so greatly indebted, I hope you will not think your-
self injured by such a declaralion from a man that
honors you, and who looks upon the liberty of put-
ting- the foIIoYsing; work under your patronage, as one
of the happy incidents of his life.
From the first moment I form.ed the design of it,
I had it in my tlioughts to address it to you ; and
indeed what couid be more natural, than that I should
be ambitious of inscribing a treatise upon the ele-
ments of philosophy, to one, who has so eminently
distinguished himself by his extensive knowledge in
that, as well as all the other branches of human
learning ?
Your great abilities in every kind, have deservedly
recommended you to the notice of your king and
country, and occasioned your being courted and im-
portuned to accept those high offices of state, which
others pursue with so much eagerness, and find it
often diScult to obtain, by all the arts and endeavors
of ambition. Nor have your talents been con^.ned
to the view of your country alone. Foreign nations
have seen and admired you, and still speak with the
greatest applauses of your wise and able conduct,
wnen it was your province to act as a British minister
abroad.
4
DEDICATION.
%^ the qualities of a great statesman are not those
aione by which you have rendered yourself ilkistri-
ous. The virtues of private life no less actuate and
adorn your whole behavior, and add a new dignity
to the high station to which your merit has raised
you. Affability, complacency of manners, and, above
ail, an extensive humanity and benevolence, which
takes pleasure in doing good, are distinguishing parts
of your character, and have contributed no less than
your other extraordinary endowments, to that uni-
versal acknov/ledgement v/hich is paid you by your
count ly.
Tliat you may long live to be an ornament and
blessing to the nation, and to enjoy the pleasure
which arises from a consciousness of the esteem and
approbation of all good men, is the sincere and hearty
prayer of,
Sir,
Your most obliged^ aiid 7nost obedient
Humble Sci'vant,
V/. DUNCAN,
■ [ 5 ]
INTHODUCTION.
Sec. I. — Importance of the Knonvledge of Ourselves,
O.
F all the human sciences, that concerning man is cer-
tainly the most worthy of man, and the most necessary part
of knowledge. We find ourselves in this .world surrounded
with a variety of objects : we have powers and faculties fitted
to deal with them, and are happy or miserable in proportion,
as we know how to frame a right judgment of things, and
shape our actions agreeably to the circmnstances in which we
-are placed. No study, therefore, is more important than
that which in'rroduces us to the knowledge of ourselves.
■ Hereby we become acquainted with the ex;ent and capacity
of the human mind ; and learning to distinguish what ob-
jects it is suited to, and in what manner it must proceed in
order to compass its ends, Ave arrive by degrees, at that just-
ness and truth of understanding, wliich is the great perfecdon
of a rational being.
Sec. IL — Di^erjent gradatijns of Perfecticni hi Things.
If we look attentively into things, and survey thein in thei**
full extent, Vv'-e see them rising one above another in variou^ -
degrees cf eminence. Among the inanimate parts of matter*
some exhibit nothing vv-orthy our attention : their parts seem
as ic were jumbled together by mere chance, nor can we dis-
cover any beauty, order, or regularity in their composition.
In others, we discern the finest arrungement, and a certain
elegance of contexture,^that makes us ainx to them a notion
cf vrofth and excellence. Thus metals, and precious stones,
are conceived as far surpassing those unformed m.assescf
earth, that lie eveiy where exposed to viev/.. If we trace na-
ture onward,- and pursue her through the vegetable and animal
kingdoms, we find her still multiplying her perfections, and
rising, by a just gradation, from mere m-echanism to percep-
tion, and from perception, in ail its various degrees, to reason
and understanding.
Sec. III. — Usefulness of Culture^ and particularly cf
the Study of Logic.
But though reason be the boundary by which man is distin- ^
guished from the other creatures that surround him, yet we arj '
V i
vi INTRODUCTION.
far from finding it the same in all. Nor is this inequality to
1)6 wholly ascribed to the original make of men's minds, or
the diiference of their natural endowments. For if we look
abroad into the several nations of the world, some are over-ruu
w*ith ignorance and barbarity ; others ficurish in learning and
the sciences : and wliat is yet more renaarkable, the sam^a
people have in different ages, been distinguished by these very
opposite characcers. It is therefore by culture, and a due ap-
plication to the poY.-ers of our minds, that we increase their
capacity, and carry human reason to perfection. Where this
method is followed, knowledge and strength of understand^
ing never faU. to ensue ; v.^here it is neglected, we remain ig-
norant of our own w'orth ; and those latent qualities of the
soul, by which she is fitted to survey this vast fabric of the
world, to scan the heavens, and search into the causes of
things, lie buried in darkness and obscurity. No part of
knowledge, therefore, yields a fairer prospect of improveinent,
than that which takes account of the understanding, examines
its powers and faculties, and shews the ways by vvhich it
comes to attain its various notions of things. This is proper-
ly the design of Logic, which may be jusdy styled the history
vi the human mind, inasmuch as it traces the progress of our
knov.dedge, from eur first and simple perceptions, through aU
their diSerent combinations, and all those num.erous deduc-
tions that result from variously comparing them one with an-
other. It is thus that we are let into the natural frame and
contexture of cur ov.ni m.inds, and learn in what manner ws.
ought to conduct our thoughts, in order to arrive at truth, and
avoid error. We see how to build one discovery upon anoth-
er, and, by preserving the chain of reasonings uniform and un-
broken, to pursue the relations of things through all their la-
byrinths aiid windings, and at length exhibit them to the view
of the soul, with all the advantages of light and conviction.
Sec. IV. — Operation.^ of the Mind.
But as the understanding, in advancing from one part of
knovvdedge to another, proceeds by a just gradation, and ex-
erts various acts, according to the diJerent progress it has
made, logicians haive been careful to note these several sreps,
and have distinguished them in their writings by the name of
the operations of the mind. These they nsake foiu- in num-
ber, and agreeably to that have divided the v.hole system of
logic into four parts, in vrhich these acts are severally explain-
ed; and the conduct and procedure of the mind, in its differ-
INTRODUCTION. y'n
ciit stages of improvement, regulated by proper rules and ob-
servations. Now-, in order to judge how far logicians have
f-Uo^ved nature, in this distinction of the powers of the un,
derstanding, let us take a shore view of the mind, and the
iTianner of its progress, according to the experience we have
of it in ourselves, and see whither the chain of our own thoughts
v/ill without constraint lead us.
Sec. V. — Perception^
First, then, we find ourselves surrounded with a variety of
©bjects, which, acting diiferently on our senses, convey distinct
impressions into the mind, and thereby rouse the attention
and notice of the understanding. By reflecting, too, on what
passes within us, we become sensible of the operations of om*
own minds, and attend to them as a new set of impressions.
But in all tliis there is only bare consciousness. The mind,
vx^thout proceeding any further, takes notice of tiie impres-
sions that are made upon it, and views tilings in order as they
present themselves one after anotlier. This attention of the
utiderstanuing co the objects acting upon it, whereby it be-
comes sensible ot the impressions they make, is called, by lo-
gicians, perception ; and the notices themselves, as they ex-
i.st in the mind, and are there treasured up to be the materi-
als cf thinking and knowledge, are distinguished by the name
ti' ideas.
Sec. VI. — Judgment,
But the mind does not always rest satisfied in theb are view
and contemplation of its ideas. It is of a more active and
busy nature, and likes to be assembling them together, and
comparing them one with another. In this complicated view
of things, it readily discerns, that soine agree and others dis-
agree, and joins or separates them, according to this percep-
tion. Thus, upon comparing the idea of two added to tv,-o>
, with the idea of four, we, at first glance, perceive their agree-
Kient, and thereupon pronounce that t'.vo and two are equal to
four. Again, that white is not black, that five is less than
.seven, are truths to vrhich we immediately assent, as soon as
V. e compare those ideas together. This is the first and sixit-
p-est act of the mind, in determining the relation of things,
vvhen, by a bare attention to its own ideas, coniparing any
two of them together, it can at once see liov,- far they are con-
nected or disjoined. The knowledge thence derived is called
I'ltuiii-je^ as requiring no pains or examination ; and the act
viii INTRODUCTIOM.
of the mind assembling its ideas together, and joining or dis-
joining them, according to the result of its perceptions, is vrhat
logicians term jndgjmr.t.
Sec. VII. — Reasoning.
Intuition affords the highest degree of certaint}' ; it breaks
in witii an irresistable light upon tne understanding, and leaves
no room for doubt or hesitation. Could we in all cases, by
thus putting two ideas together, discern imniediatel}"- their
agreement or disagreement, we should be exempt fpom error,
and ail its fatal consequences. But it so ho-ppens, that many
of ovu- ideas are of such a nature, that they cannot be thus ex-
amined in concert, or by any immediate application one to
another ; and then it becomics necessary to rind out scm.e oth-
er ideas that will admdt of this application, that by means of
them we may discover the agreeiVient we search for. Thus
the mind wanting to know the agreement or disagi-eement in
extent between tvv^o enclosed fields, w-hich it cannot so put to-
gether as to discover their equality or inequality by any im-
mediate comparison, casts about for some intenr^ediate idea,-
which, by being applied iirst to the on8,"'^nd then to the oth-
er, will discover the relation it is in quest of. Accordingly it
assum.es some stated length, as a yard, 2«c": and measuring the
fields one after the other, comes by tXat me?.ns to the knowl-
edge of the agreement or disagreemicnt in question. The in-
tervening ideas made use of on these occasions, are called
proofs ; and the exercise of the mind in finding them out, and
applying them for the discover}'' of the truths it is in search
cf, is what we term reasonhi^-. And here lee it be observed,
that the knowledge gained by reasoning is a deduction from
oiu- intuitive perceptions, and ultimately founded on them.
Thus in the case before mentioned, having found by measur-
ing, that one of the fields m^akes three-score square yards, an^l
the other only fifty-five, v/e thence, conclude, that the first
field is larger than the second. Here the two first perceptions
are plainly intuitive, and gained by an immediate application
of the naeasure of a yard to the two fields, one after another.
The conclusion, though it produces no less certain knowledge,
yet differs from the others in this, that it is not obtained by
an immediate comparison of the ideas contained in it, one
with another, but is a deduction from the two preceding judg-
ments, in v.-hich the ideas arc severally com^pared v/ith a third,
and their relation thereby discovered. Yv'e sec, therefore,
that reasoning is a much mors ccmplicated act of the mind-
INTRODUCTION. ix
than simple judgment, and necessarily presupposes It, as be-
ing ultimately founded on the perceptions thence gained, and
implying the various comparisons of them, one with another.
This is the great exercise of the human faculties, and the
chief instrument by Avhich we push on cur discoveries, and
enlarge our knowledge. A quickness of mind to find out in-
termediate ideas, and apply them skilfully in detemiining the
relations of things, is one of the principal distinctions among
men, and that which give some so remarkable a superiority-
over others, that we are apt to look upon them as creatures
cf another species.
Sec. yni.^Ma/iod.
Thus far we have tr?.ced the progress of the m.ind in think-
ing, and seen it rising by natural and easy steps from its first
and simple perceptions, to the exercise of its highest and most
distinguishing faculty. Let us now view it in another light,
as enriched with knowledge, and stored with a variety of dis-
coveries,^ acquired by a due application of" its natural powers.
It is obvious to consider it in these circumstances, as raking a
general survey of its whole stock of intellectual acquisitions,
disposing them under certain heads and classes, and tying
theni together, according to those connexions and dependen-
cies it discerns between them. It often happens, in carrying
on our enqmries from subject to subject, that we stumble upoii
•unexpected truths, and are encountered by discoveries which
our present train of thinking gave no prospect cf bringing in
our way. A man of clear apprehension, and distinct reason,
who, after due search and examination, has mastered any part
of knowledge, and even made important discoveries in it, be-
yond what he at first expected, will not suffer his thoughts to
lie jum.bled together in the same confused manner as chance
offered them ; he will be for combining them into a regular
system, where their mutual dependence may be easily traced,
and the parts seem to grov/ one out of another. This .is that
operation of the mind, known by the nam.e of disposition or
method, and com.es in the last in order, according to the di-
vision of the logicians, as presupposing some tolerable mtea-
sure of knowledge, before it can have an opportunity of e.\-
erting- itself in any extensive degree.
B
X INTRODUCTION.
Sec. IX. — 'Perception and Judgment terms of a very
extendve signification.
We see, then, that this fourfold distinction of the powers of
the mind, in.perception, judgment, reasoning, and disposition,
as well as the order in which they are placed, have a real foun-
d?,tion in nature, and arise from the method and procedure of
our own thoughts. It is true, there are many other actions
and iTiodjiica^ions of the understanding, besides those above
mentioned, as believing, doubting, assenting, &c. but these are
all implied in the act of reasoning, in the like manner, as com.-
prehending, abstracting, remembering, iTiay be referred to the
lirst op'ra,tion of the mind, or percepvion. This vs-ill appear
more fully in the sequel, when we conie to handle the several
parts of logic separately : at present we shall content ourselves
with this general account of things ; only it seems necessarv
to observe, that ptrception and judgment, in the propriety of
the English tongue, have a inuch more extensive signification
than logiciai%s commonly allow them. We not only perceive
the ideas in bur own minds, but we are said also to perceive
their agreem.ent or disagreement ; and hence arise the com-
mon phrases of intuitive perceptions, perceptions of trudi,
and of the justness of arguments of proofs ; where it is mani-
fest, that the word is a^:)piied not only to our judgments, but
also to our reasonings. In a word, v,-h?.tever comes under
the vie\v of the mind, so as to be distinctly represented and
taken notice of, whethei anidea, proposition, chain of reason-
ing, or the order and connexion of things, is thereby rendered
an ol:iject of percep don, and gives employment to this frst and
rnost simple of our faculties. In like manner, the viordjudg-
onent, is seldom, in common discourse, confined to obvious
and self-evident truths. It rather signiiies those conjeciures
and guesses that we form, in cases which admit not of un-
doubted certainty, and wheje we are left to determine by coiii-
paring the various probabilities of things. Thus a man of
sagacity and penetration, who • sees far into the humours and
passions of mankind, and seldom mistalces in the opinions he
frames of characters and actions, is said to judge well, or
think judiciously. -For these reasons, it might not be im-
prvOj;)er'to change the common names of the two first opera-
tions of the mind, calling the one simple apprehension, and the
other i'ltuition ; which two words seem belter to express their
nature, and the manner in wh.ich they are conversant about
their several objects. This accurc-icy of distingtiishing, where
IXTRCDUCTION. xi
there is any the least dinerence, is in a peculiar manner neces-
sary in a treatise of logic, as it is the professed design of that
science, to teach us how to form clear and distinct notions of
thing?, and thereby avoid being misled by their similitude or
resemblance.
Sec. X. — Logic divided into Four Parts. .Its Use/id-
71 ess and Excelienci'.
Having thus given a general idea of the four operations of
the mind, and traced their connexion and dependence upon
one another, I would next observe, that in consequence of this
division of the powers of the understanding, Icgic is also divid-
ed into four parts, which treat severally of tht^se acts, and give
rules and directions for their due conduct and regulation.
The operations themselves we have from nature ; but hov/ to
exert them justly, and employ them with advantage in the
search of truLU,*is a knowledge that m.ay be acquired by study
and observation. It is certain, that we nieet with false rea-
sonings as well as just. Some men are distinguished by an
accuracy of thinking, and a happy talent of unravelling aini
throwing light upon the most obscure and intricate subjec'-s.
Others confound the easiest speculations ; their understand-
ings seem to be formed awry, and they are incapable of either
conceiving clearly themselves, or making their thoughts in-
telligible to orhers. If then we set ourselves carefully to ob-
serve what it is that makes the one succeed so %>, ell, and hovr-
the others come to miscarry, these reniarks v/iil furnish us
with an art of the highest use and excellency in the conduct cf
life. Now this is the precise business of lojic-^to explain the-.
jTature of the human mind, and the proper manner of conduct-
ing its several powers, in order to the attainment of truth and
knowledge. Ic lays open those errors and mistakes we ar^
apt, through inattention, to run into, and teaches us how to
distinguish between truth, and what carries only the appear-
ance of it. By this means, we grow acquainted widi the na-
ture and force of the understanding, see what things lie within
its reach, where we may attain certainty and demonstration,
and when we must be contented with bare probability. These
considerations sufficiently evince the usefulness and benefit of
this science, which ought to be established as the foundation
and ground-work of all our other knowledge, if we really wish
to succeed in our enquiries. But we shall now proceed to treat
of i'S parts separately, according to the division given of
theiij above.
ELEMENTS of LOGIC
BOOK I.
OF SIMPLE APPREHENSION, OR PERCEPTION.
CHAP. I,
OF THE ORIGINAL OF OUR IDEAS.
Sec. I. — Shnple jifi/irehension and Ideas.
X HE first thing we observe, when we take a view of
what passes within us, is, that we are capable of re-
ceiving impressions from a variety of objects ; that
distinct notices are thereby conveyed into the under-
standing ; and that we are conscious of their being
there. This attention of the mind to the cbjects act-
ing upon it, is what we call simple apjirehtunon^ and
is, in fact, the mind itself taking a view of things, as
represented to it by its ov/n consciousness. It is by
this means that tve come to be furnished with all those
ideas about which our thoughts are employed. For
being sensible of the impressions made upon us, and
attending to the perceptions they bring, we can renew
them again upon occasion, even when the objects that
first produced them are removed. No^y, our ideas
a.re nothing else but these renev>-ed representations of
what v:t have at any time perceived and felt, by means
of v/jiic'-' :mng,s are agjan brought under the vieAV of
the mind, and seem to have a kind of existence in it.
14 DUNCAN'S ELEMENTS
It is true, we can upon many occasions combine our
ideas variously together, and thereby foiTn to our-
selves representations of things that never had an ex-
istence in nature, as when we fancy a centaur, or a
golden mountain ; but it is still certain, that the origi-
nal ideas, out of vvdiich these are made, are such as
has been conveyed into the mind by some former im-
pressions. It remains therefore to enquire how we
come by our first notions and perceptions of things.
Whence does the understanding derive these original
impressions and characters, which it can combine in
so many different ways, and represents to itself, un-
der such infinite varieties ? To this I answer, that if
w^e attend carefully to what passes in our minds, we
shall observe two inlets of knovv ledge, from whence,
as from two fountains, the understanding is supplied
with all the materials of thinking.
Sec. II. ''111 our original Ideas derived either from
Sensation^
First, out^vard objects, acting upon our senses,
rouse in us aA*ariety of perceptions, according to the
din'erent manner in which they afilect us. It is thus
that we acquire ideas of liglit and darkness, heat and
cold, sweet ^lud bitter, and all those other impressions
which we term sensible qualities. This great source
and inlet of knowledge is com-monly distinguished by
the name of sensation, as comprehending all the no-
tices conveyed into the mind, by impulse made upon
the organs of sense.
Sec. III.— Or Rejiection,
But these ideas, numerous as they are, are wholly
derived to us from without : there is therefore yet an-
other source cf impressions, arising from the mind's
attention to its own acts, when, turning inwards upon
itself, it takes a view of the perceptions that are lodg-
OF LOGIC. 15
ed there, and the various Vv-ays in which it employs it-
self about them. For the ideas furnished by the senses,
give the mind an opporlimity of exerting its several
powers ; and as all our thoughts, under whatever
form they appear, are attended witli consciousness,
hence the impressions they leave, v/hen we com.e to
•turn the eye of tlie soul upon them, enrich the under-
standing v.'ith a new set of perceptions, no less distinct
than those conveyed in by the senses. Thus it is that
we gej: ideas of thinking, doubting, believing, willing,
&c. vrhicix are the difierent acts and workings of our
minds, represented to us by our own consciousness.
This second source of ideas is called refiection^ and
evidently presupposes sensation ; as the impressions
it furnishes are only of the various powers of the un-
derstanding, employed about perceptions already in
the mind.
Sec. IV. — 'Risp and Progress of Human Knowledge.
These considerations, if we duly attend to them,
will give us a clear and distinct view of the naturrwl
procedure of the human intellect, in its advances to
knowledge. We can have no perception of the oper-
ations of our ovrn minds, until they are exerted ; nor
can they be exerted before the understanding is fur-
nished with ideas about which to employ them ; and
as these ideas, that give the first employment to our
.faculties, are evidently the perceptions of sense, it is
plain, that all our knowledge must begin here. This,
then, is the first capacity of the iiuman mind, that it is
fitted to receive the impressions m.ade upon it by out-
ward objects afiecting the senses ; which impressions,
thus derived into the understanding, and there lodged^
for the view of the soul, employ it in various acts of
perceiving, remembering, considering, &c. all which
are attended with an internal feeling and conscious-
ness. And thii leads us to the second step the mind
16 DUNCAK's ELEMENTS
takes in its progress towards knowledge, viz. that it
can, by its own consciousness, represent to itself these
its several workings and operations, and thereby furn-
ish the understanding with a new stock of ideas.
From these simple beginnings, all our discoveries
take their rise : for the mind, thus provided with its
original characters and notices of things, has a power
of combining, modifying, and examining them in an
infinite variety of lights, by which means it is enabled
to enlarge the objects of its perception, and finds itself
possessed of an inexhaustible stock of materials. It
is in the various comparison of these ideas, according
to such combinations of them as seem best to suit its
ends, that the understanding exerts itself in the arts
of judging and reasoning, by which the capacious
mind of man pushes on its views of things, adds dis-
covery to discovery, and often extends its thoughts
beyond the utmost bounds of the universe. Thus we
see, as it were, at one glance, the whole progress of
the soul, from the very first dawnings of perception,
till it reaches the perfection of human knowledge ;
nor shall we, among all its vast stock of discoveries,
or that infinite variety of conceptions whereof they con-
sist, be able to find one original idea which is not de-
rived from sensation or reflection, or one complex
idea which is not made up of those original ones.
Sec. Y ."Division of our Ideas into Slm^ile and Complex.
Having thus shown how the mind comes to be first
furnished with ideas, we shall next proceed to the con-
sideration of the ideas themselves, and endeavour to
give such an account of them, as will best serve to
explain their several appearances, and the manner in
which they are formed. It is evident, from what has
been said above, that they all fall naturally under these
two heads : first, those original impressions that are
or LOGIC. 17
•conveyed into the mind by sensation and reilection,
and which exist there, simple, unifDrm, and v/ithout
any shadow of variety. Secondly, those more com-
plex notions of things, that result from the various
combinations of our simple ideas, v.iietlier they are
conceived to exist of themselves, in any particular
subject, or are united and joined together bv the mind
enlarging its conceptions of things, and pursuing the
ends and purposes of knov/ledge. These two classes
comprehend our whole stock of ideas ; and, wlien
considered separately, in that order wherein they most
naturally seem to offer themselves to cur :thcughts,
will, X hope, give such a view of the conduct and m?ji-
ner of the mind, as may contribute not a little to in-
troduce us to an acquaintance with ourselves, and
make us sensible of tlie capacity and extent of the
hurnan intellect. Vv'e proceed, 'therefore, to a more
partlculai' account of this division cf cur ideas.
CHAP. II.
OF SI.MPLE IDEAS.
'. I- — ^-Ini'iic Ideas zi
^""^ class of our ideas are those which I {ii<:.
tmguish by the name of simple perception; becallse
I they exist m the mind under one unifbrm appearance
^ Witnout variety or composition. For thciieh ex^^r-
, iiai objects convey at once into the under::tandine
! many diherent. ideas, all united together, and mak^
mg as It Were one whole : yet the impressions them-
I selves -are evidently distinct, and.are conceived bv the
I 3imd, each under a form peculiar to itseli^ Thus
' tne ideas of colour, extension, and motion, may be
iS DUNCAN'S ELE1?.TENTS
tc.ksn in at one and the same time, from the same
body ; yet these three perceptions are as distinct in
themselves, as if they all proceeded from difierent
objects, or v/ere exhibited to our notice at difierent
times. \^^e are therefore carefully to distinguish be-
tween our simple and primitive conceptions, and
those different com-binations of them, which are of-
ten suggested to the mind by single objects acting
upon it. The iirst constitute our original notices of
things, and are not distinguishable into different ideas, ,
but enter by the senses simple and unmixed. They '
are also the materials, out of which all the others,
how complex and complicated soever, are formed ;
and therefore ought deservedly to be looked on as
the foundation and ground-work of our knowledge.
Sec. 11.— 'Simple Ideas of Sensation.
' Now if v/e take a survey cf these ideas, and their
several divisions and classes, we shall find them all
suggested to us, either by our senses, or the atten-
tion of the mind to what passes v. ithin itself. Thus
our notices of the difierent qualides of bodies, are all
'of the kind we call simple ideas, and may be reduced
to five general heads, accordirig to the several organs
whicli are affected by them. Colours, Sec. and sounds
are conveyed in by the eyes and ears ; tastes and
smells by the nose and palate ; and heat, cold, solidi-
ty, ^Q. by the touch. Besides these, there are oth-
ers which niake impressions on several of our sens-
es, as extension, figure, rest, and m.otion, Sec. the
ideas of wliich wc receive into our minds both by
seeing and feeling.
Sec. III.— o:;;-:J£- Ideas of Reflection, ^c.
If v.'C next turn our ". icvr upon vrhat passes within
ourselves, we sh.all find another set cf simple ideas
OF LOGIC. 19
ations of our own minds. Perception or thinking-,
and volition or AviHing, are what every man experi-
ences in himself, and cannot avoid being sensible of.
I shail only observe further, that besides all the above*
mentioned perceptions, there are others that come
into our minds by all the ways of sensation and re-
flection ; such are tlie ideas of pleasure and pain,
power, existence, unity, succession, &c. v/hich ar«j
derived into our understandings both by the action
of objects without us, and the consciousness of vrhat
v.e feel within. It is trac some of these ideas, as cF
extension and duration, cannot be conceived altogeth-
er without parts, neve'rti"!eiess, they are justly ranked
among our simple ideas ; because tlieir parts being
all of the same kind, and without the m-ixture of any
other idea, neither of tliem can be resolved into tv.o
distinct and separate conceptions. Thus they still
^answer the definition given above, of being one uni-
form appearance in the mind, with variety or plural-
ity. But to prevent confounding our simple ideas cf
space and duration, v/itli these complex modes cf
them marked out by the several measures com.m.on-
ly in use, as yards, miles, days, years, ixc. it may
perhaps be most proper to consider the least portions
of either whereof we can form a clear and distinct
perception, as the siniple ideas of that kind out of
which all their other modes and com.binations are
formed. Such an instant, or point, may be con-
ceived to be the same in respect of duration or
space, as unity is in re_spect of numbers ; and will
serve best to show, how by a continued addition or
repetition, our m.ore enlarged and complex ideas are
made up.
20 DUNCAN'S ELE^.IENTS
Sec. IV.— .SV:72,^'/.i- Ideafi have no AdmissiGn But by (ha:
iiTop.er Inlets cf Mature.
Kavlng thus given a n^eneral view of our simple
idsas, I have still two coservations to make ccncern-
ing them. The first is, thtl they are such as can
only be conveyed into the mind by the proper chan^
r.el3 and avenues provided by nature ; insomuch that
\i we are destitute m any of those inlets, by which
the impressions that produce them are want to be
iidniitted. all the ideas thence arising: are absolutely
lost to us ; nor can we, by any quickness of under-
standiujj, find a remedy for this want. A man born
blind is incaj>able of the ideas of light and colours ;
m like manner as one who is deaf can form no no-
tion or conception of sounds. Hence it appears, that
these our simple ideas are just such as nature has^
iumic-hed them, and have no dependence en our
will ; we can neither destroy them when in the un-
derstandln/j, nor i^shion or invtrnt any new one, not
taken in by the crdiiiary means of perception. So
that we here see the utmost bounds of human knovvl-
Cuge, v/hic!], however miguLy and enlarged, cannot
exceed the limits of those cur simple original ideas,
and their various combinations.
Sec. V. — They furnish ampde Materials of Kno^vljdg^.
And this lead 3 me to the second observation I
proposed to make, which is, that though the m.ind
cannot, in multiply :::g its coiiceplions of things, ad-
vance one step beyond the materials furnished it by
£ense and consciousness ; jxt as it has a pcAver ut
com!>ining, mcdifyiT:^?;, a;nd eniargingthera, in all the
chiierent ways' in which they can be put together, it
therefore finds itseif in possession of an inexhaustible
treasure of ideas, suaicient to employ it to the full
extent of ail its povvcrs, and furnish matter for ail
OF LOGIC. 2i
those yarious opinioDs, fancies, and views of thing-s,
that make up the subject of its thoughts and con-
templations. Let us but reflect upon the single idea
of unity or one, and observe v.iiat a variety of combi-
nations are formed, by continually adding it to itself ;
insomuch that the understanding finds no stop or
boundary, in its progress from number to number.'
in vrhat an infinity of different lights may extension
alone be considered I what lim.its can be set to that
endkss diversity of figures, which it is in the powxr
of the imagination to fashion and represent to itself ?
If to these we add those numberless other cornbina-
tions that result from variously compounding and
comparing the rest of our simple ideas, we shall have
little reason to complain of being limited to a scanty
measure of knowledge, or that the eiiercise cf the
human faculties is connned within narrow bounds.
But bavin? traced the proe:ress of the mind throuirh
its original and simple ideas- until it begins to enlarge
its conceptions by uniting and tying them together ;
it is nov/ lime tc take a suney of it as thus employed
in multiplying its views, that we may see by what
ssleps it advances from one degree of improvement to
another, and how it contrives to manage that infinit<e
stock of materials it finds itself possessed of.
Sec. YI.— T/ie Bivi.non rf comjiiex Ideas into those 'jJ
real ILxisiaice^ and those framed by the Aiind.
Whoever attentively considers his own thoughts,
and takes a view of the several complicated ideas that
from tiiTie to time citer themselves to his understand-
ing ; will readily observe, that m.any of them are
such as have been derived from without, and suggest-
ed by different objects affecting his perception ; oth-
ers, again, are fornied by the mind itself variously
coiTibining its simple ideas, as seems best to answer
22 DUNCAN'S ELEMENTS
those ends and purposes it has for the present in vie^.y.
Of the first kind are all our ideas of substances, as of
a man, a horse, a stone, gold. Oi the second are
those arbitrary collections of things, which we on
many occasions put together, either for their useful-
ness in the commerce of liTe, or to further the pursuit
of knowledge : such are our ideas of stated lengths,
whether of duration or space ; c.r. hours, months, miles,
leagues, 8cc. which divisions are apparently the crea-
tures of the mind, inasmuch as we often hnd them
different in different countries ; a sure sign that they
are taken from no certain and invariable standard in
nature. Many of our ideas of human actions may be
also referred to this head ; as treason, incest, man-
slaughter, &c. which complex notions v/e do not al-
ways derive from an actual viev/ of v/hat these Vv^ords
describe, but often from combining the circumstances
of them in our minds, or, which is the most usual
way, by hearing their names explained, and the ideas
they stand for enumerated. T'hcse two classes com-
prehend all our complex conceptions, it being impos-
sible to conceive any that are not either suggested to
the understanding by some real existences, or formed
by the mind itself arbitrarily uniting and compound-
ing its ideas. Vv'e shall trep.t of each in order.
CHAP. III.
07 ova IDEAS OF SUBSTANCES.
Sec. I. — Ideas of Substances^ Collections of Siiyiple Iclcasi,
held together by some unknovon support.
T
HE first head of complex ideas mentioned in the
foregoing chripter, is that of substances, which I
choose to handle before the other j becauscj as vrill
OF LOGIC. 23
aftcnvards appear, the notices derived from this source
very much help us in forming; those arbitrary collec-
tions, vrhich make up the second division. For in
many cf them we take cur hints from the reality of
things, and combine ideas that actULilIy exist togeth-
er, though often with an exclusion of others, as will be
explained wdien v/e come to treat of abstract and uni-
versal notions. It has been already observed, that
the impressions ccnveyes:! into the understanding
from external objects, consist for the most part of
many different ideas joined together, ^vhich all unite
to makeup one v>hole. These collecclolis of various
ideas, thus co-existing in the same common subject,
o.nd held together by some unknown bond of union,
have been distinguished by the name of substances, a
word v\-hich implies tlieir subsisting of themselves,
without dependenc^e (at least as far as our laiowkdge
reaches) on any other created beings. Such are the
ideas Vv e have of gold, iron, v/ater, a man, &c. For if
we fix upon any one of these, for instance, gold, the
notion under vrliich vre represent it to ourselves is
that of a body yellovr, very weighty, hard, fusible,
m.aileable, Sr.c. where we may observe, that the sev-
eral properties 'that go to the com.position of gokh are
represented to us by clear and evident perceptions ;
the union too of these properties, and their thereby
constituting a distinct species of body, is clearly ap-
prehended by the mind : but vv^hen we would push
cur enquiries farther, and know wherein this union
consists, what holds the properties together, and gives
them their self-subsistance, here v,'e f.iid ourselves at
a loss. Ilovv^ever, as we cannot conceive qualities.
Without at the sraiie time supposing some subject in
which they adhere, hence we are naturally led to tbrm
the notion cf a support, which, serving as a founda-
tion for the co-existence and union of the dif^rent
1>4 DUNC/vN's ELIL^MEXTS
properties of things, gives them that separate ami
independent existence under Avhlch they are present-
ed to our conception. This support we denote by
the name substance ; and as it is an idea applicable
to all the different combinations of qualities that exist
any vrhere by themselves, they are accordhigiy all
called substances. Thus a house, a bovvJ, a stone,
&c. having each their distinguishing properties, and
being conceived to exist independent one of another,
the idea of substance belongs alike to them all.
Sec. II. — The Division of Modes into Essential and
Accidental.
In substances, therefore, there are two things to be
•considered : first, the general notion of self-subsist-
ence, which, as I have said, belongs equally to them
all ; and then the several qualities, or properties, by
v.hich the different kinds and individuals are distin-
guished one from another. These qualities are oth-
erwise called modes, and have been distinguished in-
to essential and accidental, according as they are per-
ceived to be separable or inseparable from the subject
to which they belong. Extension and solidity are es-
sential modes of a stone ; because it cannot be con-
ceived without them ; but roundness is only an ac-
■cidental mode ; as a stone may exist under any shape
or figure, and yet still retain its nature and other
properties.
'Sec. III. — The Kc'ion of Self-Siib&ictcnce inseparable
from subsistence,
I might run fartlier into these divisions and sub-
division's, in which logicians have been very fertile ;
but as they tend little to the advancement of real
knowledge, and serve rather to lili the memory vvfith^
T^'ords and their s:G:niiic?itions, tlian furnish, clear and
OF LOGIC. 2S
distinct apprehensions of things, I shall not trouble
the reader with them. It is more material to observe,
that the change of properties in any substance, tho'
it oft-times changes the nature of that substance, that
is, its species or kind ; yet it never destroys the gen-
eral notion of self-existence, but leaves that equally
clear and applicable, as before any such alteration
happened. Wood, by the application of fire, is turn-
ed into charcoal ; but charcoal, however different
from vrood, is still a substance. In like manner, wax
may be converted into flame and smoke ; a human
body will moulder into dust : yet these alterations
destroy not their being or existence : tliey are still
substances as before, though under a different form
and appearance. In the several experiments made
by chemists, bodies undergo many changes, and put
on successively a great variety of different shapes,
and yet, by the skill and address of the operator, they
are often brought back to their first and pi-imitive
form. Vv'hat alteration can we suppose the nre, or
the application of any- other body, to make, miless on
the configuration, tey.ture, or cohesion of the minute
parts ? When these are changed, the body is propor-
tionably changed ; ^.vhen they return to their original
state, the body lil;.e>vise puts on its first and natural
appearance.
Sec. IV. — Foimd ation of the different Species of Cor-
poreal Substances.
All that is ef sential to matter, therefore, is the co-
hesion of solid extended parts : but as these parts are
capable of in/ lumerable configurations — as their tex-
ture may be t ery various, and the internal constitution
thence arising be of consequence extremely difterent
in different bodies— we may from these considerations-
conceive yjretty clearly the source and foundation of
D
26 DUNCAN'S ELEMENTS
all the different species of corporeal substances. Nor
is this a notion taken up at random, or one of those
chimerical fancies in philosophy, derived rather from
a warmth and liveliness of imagination, than observa-
tions drawn from things themselves. Do we not dai-
ly see our food, by the changes it undergoes in the
different avenues of the body, converted first into
blood, and thence employed in nourishing, building
up, and enlarging, the several parts of that wonderful
fabric ? Rain, descending from the clouds, and mix-
ing v.'ith the mould or earth of a garden, becomes ali-
ment for trees of various kinds, puts on a diversity of
forms, according to the different channels and con-
veyances through which it passes ; and at last, after
innumerable changes and tnuismutEdions, sprouts forth
in leaves, opens in buds, or is converted into the sub-
stance of the tree itself. Can Vv'e conceive any greater
difference between the component parts of gold, and
those of stone, than betv»-een the moistened particles
of garden mould, and those ne v forms and Rgures un-
der Avhich they appear, after they have been thus
fashioned by nature for the pu/poses of growth and
nourishment ?
Sec. V. — Essence of Substances nrjthing but the inter-
nal structure and constitution ;
If this be duly attended to, it will not appear won-
derful to assert, that the variety'of material substanc-
es arises wholly from the different coniiguration,
size, texture, and motion of the minute parts. As
these happen to be variously combined, and knit tc-
f^ether, under different forms, bodies put on a diversi-
ty of appearances, and convey into the mind by the
senses all those several impressions, by which they
are distinguished one from another. This internal
constitution or structure of parts from which the sev-
OF LOGIC. sr
cral properties that distinguish any substance flow,
is called the essence of that substance, and is, in fact,
unknown to us, any farther, than by the perceivable
impressions it makes upon the org-ans of sense. —
•Gold, as has been said, is a body yellow, very weigh-
ty, hard, fusible, malleable, S^c. Tliat inward struc-
tiure, and conformation of its mJnute particles, by
which they are so closely linked together, and from
which the properties above irierxtioned are conceived
to flow, is called its essence ; and the properties
themselves are the perceivable marks thai make.it
kno'vvn to us, and distmguish it from all other sub-
stances ; for our senses are not acute enough to reach
its inward texture and constitution. The parts them-
selves, as well as their arrangem^ent, lis far beyond the
utmost penetration of human sight, even when as-
sisted by microscopes, and all the other contrivances
of art.
Sec. VI. — Is \vholly unknoivn to us and serves to dis-
tinguish the Species ;
Thus, as to the essence or internal constitution of
gold, vre are wholly in the dark ; but many of the prop-
erties derived from this essence, make obvious and
distinct* impressions, as the weight, hardness, and yel-
lovr colour. Sec. These properties combined together,
and conceived as co-existing in the same common
subject, m.ake up our complex idea of gold. The
same may be said of all the other species of corporeal
substances, as lead, glass, water, &c. cur ideas of
them being nothing else but a collection of the ordi-
nary qualities observed in them.
Sec. VII. — Yet zV is nghtly presumed to be distinct in
all the several kinds.
This, hoVi^ever, ought to be observed, that though
the essence or iny, ard si;i"^^c:v.ve c: bodies is tUtcgeth-
28 DUNCAN'S ELEMENTS
er unknown to us, yet we rightly judge, that in all the
several species, the essences are distinct. For each
species being a collection of properties, which, taken
together, are different from those of every other spe-
.cies, the conformation of parts, on which these prop-
erties depend, must in like manner be different ; and
this, as we have said, constitutes the essence. Iron
and glass are evidently distinct kinds of body ; their
perceivable qualities have little or nothing common ;
ar.d therefore the inward structure or constitution
from v/hich these qualities flow, cannot be the same in
both. But after all, this is the only thing we can with
certainty affirm concerning tliese essences, which ly-
ing so wholly in the dark, we shall do well to lay them
aside in our reasonings about things, and adhere to
those more intelligible and settled ideas acquired by
joining together tlieir various properties and powers.
For thus only is true knovrledge promoted, when we
argue from kno^"\ai qualities, and not from a supposed
internal constitution, v/hich, hoAvever real in itself,
yet comes not within the reach of our faculties^ and
therefore can never be a ground to us for any discov-
eries or improvements.
Sec. VIII. — By ivhat steps nve arrive at the JSi'otions
of Immaterial K^ubstances ;
Material substance, as I have said, includes the idea
of solid, cohering, extended parts, and is divided into
different classes according to the different impressions
■made upon the organs of sense. But, besides tliese
sensible ideas received from without, v/e also experi-
ence in ourselves thinking and volition. These ac-
tions have no connexion with the known properties
of body ; nay, they seem plainly inconsistent with
some of its most essential qualities. For the mind
not only discovers no relation between tliinking, and
OF LOGIC. i9
the motion or arrangement of parts ; but it also per-
ceives, that consciousness, a simple individual act, can
never proceed from a compounded substance, capa-
ble of being divided into many. Let us suppose, for
instance, a system of matter endowed with thought ;
then either all the parts, of which this system is com-
posed, must think, which would make it not one, but
a multitude of distinct conscious beings ; or its power
of thinking must arise from the connexion of the parts
one with another, their motion and disposition, &c.
which, all taken together, contribute to the produc-
tion of tlicught. But it is evident, that the motion of
parts, and manner of combinmg them, can produce
notliing but an artful structure, and various modes of
motion. All machines of human composition, as
watches, clocks, S:c. however artfudy their pans are
set together, however complicated their structure-
though vre conceive innumerable diiTercnt motions,,
variously conjoined, and naming one into another
vv^ith an endless diversity, yet never produce any thing
but figure and motion. If a clock tells the hour a^d
minute of th^ day, it is only by the motion of the dif-
ferent hands;pointing successively at the figures mark-
ed on the hour-plate for that purpose. We never
imagine this to be the effect of thought or intelli-
gence ; nor conceive it possible, by any refinement of
structure, so to improve the comjDosition, as that, it
shall become capable of knowledge and consciousness.
The reason is plain ; thought is something altogeth-
er different from motion and figure ; there is not the
least connexion betvveen them ; and therefore it can
never be supposed to result from them.
Sec. IX. — Which Kve otherwise call S/iirits.
This then being evident, that intelligence cannot
arise from an union or combination of unintelligibla
^n DUNCAN'S ELEMENTS j
parts ; if we suppose it to belong to any system of!
matter, we must necessarily attribute it to all the
parts, of which that system is composed ; whereby,
instead of one, we shall, as was before observed, have
p. multitude of distinct conscious beings. And be-
cause matter, how far soever we pursue the minute-
ness of its parts, is still capable of repeated divisions, ;,
even to infinity ; it is plain, that this absurdity will ^
follow us, through all the suppositions that make
thought inherent in a materia.1 substance. Finding,
therefore, consciousness incompatible with the cohe-
sion of solid seperable parts, vre are necessarily led to ;
place it in some other substance^ of a distinct nature '
xind properties, which v/e call spirit.
Sec. X. — Body and Sfihit distinct Substances.
And here it is carefully to be observed, that the
several species of corporeal substances, though distin- .
guished one fi'om another, and ranked under different
names ; yet, agreeing in some com.mon properties,
-which, taken together, make up the notion of body, |
are thence all conceived to partdke of? this general
nature, and to differ only as different modifications of
the same substance. Whatever consists of solid ex-
tended ppirts, is called matter ; and as ail the various
species of body, however distinguished from one an-
other by their several properties, have yet this in
common, that they are made up of such solid seper-
abie parts, hence they fall naturally under the gener-
al denomination of material beings, and are not con-
ceived to differ, but in their form. Thus gold, anti-
mony, wood, Sec. alike partake of the notion of body ;
they are ail equally material substances, and have no
other difference, but what arises from the different
structure and conformation, 8cc. of parts, as we have
shewn above. But sfiirit is something altogether
OF LOGIC. 31
distinct from body, nay, and commonly placed in op-
position to it ; for which reason, the beings of this
class are called immaterial ; a word that implies not
any thing of their nature, but merely denotes its con-
trariety to that of matter.
Sec. XI. — There may be many varicus Species of Sub-
stances^ besides those that come iviihin the reach of
our Faculties.
Body and spirit, therefore, differ not as species of
the same substance, but are really distinct kinds of
substances, and serve as general heads under which
to rank all the particular beings that fall within the
compass of our kno^vledge. For we having no ways
of perception but sense and consciousness, can have
no notices of things, but as derived from these two
inlets. By our senses we are informed of the exist-
ence of solid extended substances ; and reiiectioii
tells us, that there are thinking conscious ones. Be-
yond these our conceptions reach not ; and therefore,
though there m.ay be many other kinds, as diiferent
from them as they are from one another, yet having
no faculties suited' to them, they are as remote from
our knowledge, as light and colours from the appre-
hension of a man born blind. I believe it will hard-
ly be doubted but the substance of the Creator differs
more from that of his creatures, than any two created
substances can from one anotlier ; and therefore when
we call God a spirit, M'e ought not rashly to presume,
that he is so in the same sense in which the human
soul is a spirit. The word is, indeed, used by us, to
denote in general all thinking intelligent substances,
in which sense God is very fitly called a spirit. But
it were the height of folly to imagine, because this
namie is applied as vrell to the mind of man as the
Creator, that therefore they partake of one commoa
52 DUNCAN'S ELEMENTS
nature, and differ only as different modifications of
the same substance. This I mention here, to check
the presumption of the human mind, always forward
to conclude, that every thing comes v/ithin its reach,
and to deny existence to whatever exceeds the conpre-
hension of its scanty and limited powers. Beings of
a superior class may enjoy many ways of perfection
unknown to us, from which they receive notices as
different from those in our minds, as the ideas we
apply to spirit are from the ideas v,'e apply to body.
Solid and thinking beings are, it is true, the only
ideas of substance that we are able to frame ; but
this is no more an argument against the existence of
other kinds, than the v/ant of the ideas of light and
colours in a blind man v/ould be a good argument a-
gainst the reality or possibility of such perceptions^
Sec. XII. — Difference in the manner of conceiving
Corporeal and Sjiiritual Substances.
Before I dismiss this subject, it may not be im-
proper to take notice of a remarkable difference as
to the manner of our conceiving corporeal and spirit-
ual substances. Those of the first kind convey them-
selves into the mind by impressions made upon the
organs of sense ; and as these impressions are difler-
ent in different bocfies, the ideas they produce must
of course vary in proportion. Thus we get precep-
tions of distinct powers and properties, and range bo-
dies into classes, according as we find them to agree
or disagree in their observable qualities. But it is
not so in our notion of spirits ; for having no con-
ception of their powers and operations but by what
we feel and experience within ourselves, we cannot
ascribe to them properties or ways of knowledge,
distinct from those suggested to us by our o^vn con-
sciousness. And hence it is, that though we readily
OF LOGIC. "SS
oivn there may be various r?Jiks cf spiritual beings,
•yet we are uot to imagine theiA divided from one cj\-
-otiier by any diversity of powers and operations, but
merely by possessing the same powers, Sec. in a
higher or' lower degree. It is not, however, repug-
nant to reason, that they should be distinguished by
their several properties in like m.anner as sensible
•thin<-'-s are by tiie d-fferent q<ialities obcervable in
•them ; but properties of intellectual natures, distinct
from those of our 0-^-1 minds, being altogether re-
mote from our conception, cannot serve as a means
tvhereby to distinguish their different orders. We
are therefore necessitated to conceive of them in a
manner suited to our way of knowledge ; and ^vhen
vre would rank them into species, according to the
degrees of superiority theyare imagined to possess hi
the scale of being, we ascribe to them v/hat we find
most excellent in ourselves, as knov/ledge, thinking,
foresight, Sec. and those in different measures pro-
portioned to the station peculiar toeacti rank or spe-
cies. But that this is a very imperfect way of dis-
tingtiishing the various orders cf intellectued beings,
will not, I think, need many words to make it ap-
pear ; especially if we consider, that the manner of
comm.unicating their thoughts, without the interven-
tion cf bodily organs, is a thing to us altogether in-
comprehensible) and necessarily leads us to suppose,
that they have ways of perception and knov/jcdge'
vvhich our faculdcrs cannot give us any notice o£
Sec. XIII. — The donnas of Knorjlcdge in our /ircsaU
state very ?zarroiu.
But I shall not pursue these reflections farther ;
wdiat has been said sufncingto give us some Uttle in-
«jip:ht into the extent and capacity of our ov/n minds ;
to convhice us that our present state will not admit of
E
,34 DUNCAN'S ELEMENTS
a perfect and adequate comprehension of things ; an^
to let us see, that there may be other v/ays of knowl«
edge, beyond the reach of the faculties we now enjoy ;
which yet, in succeeding stages of our existence, we
may arrive at, when, being freed from the present
cumbersome load of the body, we shall mount up to
stations of greater eminence, and advance by a perpet-
ual series of approaches towards him, who. is the
standard of perfection and happiness.
CHAP. IV.
OF .IDEAS FRAiVrEX) BY THE MIND.
Sec. I.- — In framing many comfilex Ideas^ the Mind is
wholly active^ andfiroceeds by a voluntary choice.
irliTHERTO we have considered only such combi-
nations of cur simple ideas as have a real union in na-
ture, and are suggested to the mind, by things them-
selves variously aiiecting our perception : it is now
time to take a view of the other class of our complex
notions ; I mean those arbitrary collections of differ-
ent ideas, v,iiich v/e on many occasions bring together '
by that power vrhich v/e hnd in ourselves, of uniting,
comparing, and diversifying our notices of things. In
the reception of simple ideas, and even in those of
substances, the understanding is wholly passive,
and the perceptions produced correspond to the
impressions made upon it. When we see a house,
or a tree, they necessarily appear each under
its proper form; nor is it in our power to receive
from these objects other ideas than what they are fit-
ted to produce. But in this second class of complex
conceptions, the mind acts voluntarily and of choice ;
it conibines only such ideas us are supposed best to
OF LOGIC. 35
suit its present purpose ; and alters or changes these
combinations, by inserting some, and throwing out
others, according as the circumstances of things re-
quire their being viewed in different lights. Now as
this is by far the most comprehensive branch of our
ideas, and inckides those that most frequently occur
in the search and pursuit of knowledge, I shall en-
deavour to treat them in the exactest order and meth-
od ; and for tliat purpose range theill under several
heads, according to the different acts of the mind ex-
erted in framing and putting them together.
Sec. II. — Three several Acts exerted by the Mind i:i
framing its arbitrary IcUas, viz. Composition ;
These acts may in the general all be reduced to
three. 1. Ccmposition, when we join many sim.ple
ideas together, and consider them, as one picture or
representation. Such are our ideas ct beauty, grati-
tude, a furlong, 8cc. And here let it be observed, that
the mind sometimes confines itself to the various con-
skieration of the same idea, and, by enlarging it in
different degrees, exhibits it under a diversity of forms.
Thus by adding units together, in distinct separate
collections, vre come by the several combinations of
numbers, as a dozen, a score, a million. At other
times we unite perceptions of different kinds ; in
which case the composition is more manifest, and
the idea itself becomes of course mgre complicated.
Harmony, for instance, is a compound idea, made up
of many" different sounds united ; all which the mu-
sician must have, and put together in his mind, be-
fore the ear can be entertained with the actual per-
formance. Now although the act of the mind is in
some measure exerted in the framing of all our com-
plex notions, yet as many of them mclude certain
limited and panieular considerations; arising from
ether optraticr.s cf the mind employed about thcmj
it is necessary to take .account of these acts also, if
we would conceive clearly tiie manner in wxiich the
several Lpecies of o^r compound ideas are fonxied.
Sec. III. — Abstraction ;
2. The next operation therefore of the mind, about
its ideas, is 2bi,tracticv^ whcPi we separate from aijy
of our coDceptiates ail those circumstances that reri-
der it pailicniar, or the representative cf a single de-
terminate object ; by which means. Uistead qi stand-
ing for an individual, it is made to denote a whole
rank cr class of things. Thus upon setir.g, for in-
stance, a square or circle, we leave out the consider-
ation of their bulk, and every thing else peculiar to
them., as they imm.ediately aiTectour sight, retaining
only the notion of their fjgvire and shape. - In this
manner we get our general ideas ; for such naked ap-
pearances, separated from the circumstances of time,
place, tic. serve the mind as standards by which to
rank and denominate particular objects. When there-
fore vve m^eet with a figure answering to that shape
and form we ha.d hSxl up in our understandings, it is
imm.ediately referred by the mind to this pattern,
and called by its name, which by this means becom.es
proper to the v/hcle species. Thus a square, or cir-
cle, are urdv-rsal terms, common to all figures 'of
that particular shape, and alike applicable to them
wherever they'^xist : in like manner as the ideas
themselves, are general^ and representatives of aii
the kind.
g^n_ lY , 4nd Co7nparison.
3. Tiie third and last act of the mind about its
ideas, is the conijiurhig them one with a.nctl!cr> v. hen
we carry our consideration of things beyond tiie ob-
OF LOGIC. 37
jtcts themselves, and examine their respects and cor-
respondences in reference to other things which the
mind brings into view at the same time. It is thus
we sret ail our ideas of rclatio?::, as of greater, less,
older, youn2:er, father, son, and innumerable others-
This threefold vie^v of cur ideas, as either com.pound-
ed of many others put together, or made universal
by the abstraction of the mind, or as representing the
various relations and habitudes of things, will give us
LU opncrtunitv of observing whatever is most curious
and useful in this fondaniental branch of knoAviedge,
ti'd of explaining the ma.nner and procedure of the
understanding in enlarging its vie tv 3, and multiply-
ins- the objects of perception. That we may there-
fore conceive of this matter with the greater order
and clearness, we jihall make each of these several
itdeas the subject of a distinct article.
ART. I.
OF CGI'IPOUXD IDEAS.
See. l.—Comf.cund Ideas considered here mcrehj as
Combinations of the Understandi7:g.
T T 7
VV E be;2;in therefore with those ideas wliich may
be properly termed compound., as being derived from
that power tlie mind has of uniting many conceptions
iiito one. Though this class comprehends^^in some
sort, all our complex notions, yet they are at present
considered merely as tliey arc combinatioiis of the
understanding, and with a wiew to those particular
ideas out of which they are framed. Here, as was
already observed, the mind scmecimxes proceeds hj
enUrging and diversifyhi^ the same idea ; at other
times it brings together ideas of diaerent kinds ; and
53 DUNCAN'S ELExMENTS
m both ways finds infinite scope and variety. But
that we may follow the natural procedure of the in-
tellect, and trace it in its advances from simple to
inore complicated acts, we shall first take a view of
It as employed about one and the same idea, where
• perhaps we may meet with such instances of address,
inanag-ement and contrivance, as will appear perfectly
r.stonishing to one who has never set himself seri-
ously to consider the manner and conduct of his own
mind.
Sec. II. — U?2Uy the Original and Foundation of all our
Ideas of jYumbcr.
The m.ost obvious and simple idea we have, is that
of unity or one. By adding- it to itself continually,
and retaining^ the several collections in our minds,
we come by all the different combinations of num-
bers, in which we readily perceive an endless diver-
sity. All these ideas are nevertheless evidently dis-
tinct among themselves, the addition of a single unit
constituting a number as clearly diSerent from that
immediately before it, as any two the most remote
Ideas are from one another.. But that the understand-
ing may not lose itself in the consideration of those
infinite combinations of which unity is capable, it pro-
ceeds by regular steps ; and beginning with the orig-
inal idea itself, pm'sues it through all its varieties, as
they are formed by the repeated continual addition of
unit after unit.. Thus numbers are made to follow
one another in an orderly progression, and the sev-
eral successive collections aj;e distinguished by par-
ticular names.
Sec. III. — The artfid comfiosiiion of the names of JK'um-
bers a great helji to our conceptions ;
And here v,e may take notice of a wonderful arti-
&ce made use of by the niind, to facilitate and help it
OF LOGIC. ^9
forward in its conceptions. For as the advance from
number to number is endless, were they all to be
xiistinguished by different denominations that had no
connexion or dependence one upon another, the mul-
titude of them must soon overcharge the memory,
and render it impossible for us to go any p-reat way
in the progress of num.bering. For this reason it is
-so contnved, that the change of names is restrained
to a few of the first combinations, all the rest that
follow being marked by a repetition of the sam.e terms,
variously compounded and linked together. Thus
thirteen is ten and three, fourieen,.ten and four, and
so on to twenty, or two tens, when wq begin again
with one, tvro. Sec. until we advance to thirty, or
three tens. In this manner the progression contin-
ues ; and when we arrive at ten tens, to prevent con-
fusion by a two frequent repetition of the same word,
that sum is distinguished by the name of a hundred.
Again, ten hundred is called a th{|isand, at vrhich pe-
riod the computation begins anew, running through
ail the former combinations, as ten thousand, a hun-
dred thousand, ten hundred thousand ; v^^hich last
collection, for the reasons mentioned above, has the
name of a million appropriated to it. With this mill-
ion, we can begin as before, until it is repeated a mill-
ion of times ; when, if we change the denomination
to billions, and advance m the same manner throuo-h
trillions, quartillians, the series may be carried on
vdthout confusion, to any length we please.
Sec. IV. — Jnd cf. the firindfial Reasons that our Ideas
of ^, umbers are so remarkably distinct.
This artful combination of names to mark the grad-
ual increase of numbers, is perhaps one cf the great-
est refinements of the human understanding, and
particularly deserves our admiration ior the mamier
•40 IDUNCAN's ELEMENTS
of the composition ; the several denominations bein?^
so contrived as to distingTiish exactly the sca^jes of
the progression, and point out the distance from the
beginning of the series. By this means it happens,
that our ideas of numbers are of all others the m.ost
accurate and distinct ; nor does the multitude of units
assembled together, in the least puzzle or confound
the understanding. It is indeed amazing, that the
mind of man, so limited and narrov^ in its views,
should vet here seem to shake off its natural vveak-
ness, and discover a capacity for managing with ease
the most bulky and formidable collections. If we
enquire particularly into the reason of this, we shall
find it wholly owing to the address of the mind in thus
distinguishing numbers by different names, accord-
ing to the natural order of progression. For as those
names are made to grov/ one oiit of another, they may
be aptly compared to' a chain, all whose parts are
linked together by an obvious and visible connexion.
Hence it comes to pass, that when we fix our thoughts
upon any number,'' however great and seemingly un-
managable ; yet, if it is once determined to a particu-
lar name, %ve iind it easy to run back through all the
stages of the progression, even till we arrive at unity
itself. By this means we see, with a single glance of
our minds, not only, the two extremes of the nurr.ber
under consideration, but also the several intermcdicite
parts, as they are united to make up the whole.
ggc. V. ^-s they help us to a clear Ptrctpnon of the
interjactnt Paris.
Nov/ it is to this clear and accurate view of the in-
terjacent ideas, that we ov/e our so distinct percep-
tion of the various combinations of numbers. And
indeed v/e may observe, in tlie general, that all our
ideas of quantity, especially when thej grow to be very
OF LOGIC. 4i
large, are no otherwise ascertained than by that per-
ception v,"e have of the intervening parts, if I may so
say, between the extremes. When we look at any
object considerably distant from us, if we have a clear
view of the interjacent lands and houses, we are able
to determine pretty nearly of its remoteness ; but if,
without such a kncvrledge of the intervening spaces,
we should pretend to judge of the distance of objects,
as V, hen we see the spire of a steeple behind a wall, or
beyond a mountain, every one's experience is a proof
hovv^ liable we are, in these cases, to be deceived. Just
so it is in judging of duration. When we carry back
our thoughts to any p^.ct period of cur lives, without
consideration of the number of years or months, v/e
fxud that our idea of the time elapsed grov/s more dis-
tinct, in proportion as we become sensible of the in-
termxcdiate parts of our existence. At first we are apt
to judge the distance extremely short ; but when we
set ourselves to consider our several successive
thoughts and actions, the idea of the duration grows
upon us, and continues to increase as the attention of
the ^nd brings new periods of life into view.
Sec. VI. — J'llihout narnes^ we cannot make any jiro^
gress in Numbering.
Hence it will be easy to conceive how much the
mind is helped forward in its perception of number, by
that ready comprfchension of all the several stages in
a progression, which peculiarly belongs to ideas of
this class. But this, as I nave before intimated, we
derive from the orderly series and connexion of nam^es,
insomuch that where they cease, the computation of
num/Oers also ceases with them. We can have no
idea of any sum, without a knoT>1edge of all the terms-
that go before, according to the natura][^rdcr in which
they ioilovr one another ; so that he who cannot, in »
F
42 DUNCAN'S ELEMENTS
regular way, count to ninety-nine, will never, while
that incapacity continues, be able to form the idea of
a hundred ; because the chain that holds the parts
together, is to him wholly unserviceable, nor can he
represent to his mind the several interjacent com-
binations, v/ithout which it is impossible in this case
to arrive at a distinct perception.
Sec.VII. — The great advantages of Address in Class^
ing our complex Conceptions.
I have insisted the more largely upon this, not on-
ly because it is by number that we measure ail other
things, as duration, extension, motion, &c. but also
because it lets us into the most natural view of the
conduct and procedure of the understanding, and
Biakes us sensible of the great art and address that is
necessary in the classing our very com.plex concep-
tions. Ke that can so put together the component
parts of an idea, as that they shall lie obvious to the
notice of the mind, and present themselves, when oc-
casion requires, in a just and orderly connexion, Aviil
not find ii very difficult to obtain clear and accurate
perceptions, in most of those subjects about A^.ich
our thoughts are conversant. For the great art of
knowledge lies in managing with skill the capacity
<if the intellect, and contriving such helps as, if they
strengthen not its natural powers, may yet expose
them to no unnecessary fatigue, by entangling and
perplexing them vrith considerations remote from the
business in hand. When ideas become very complex,
and by the multiplicity of their parts grow too un-
vdeldly to be dealt with in the lump, we must ease
the view of the mind, by taking them to pieces, and
setting before it the several portions separately, one
after another.. By this leisurely survey we are ena-
bled to. take in the whole ; und if we can draw it into
OF LOGIC. 45
swell an orderly combination, as will naturally lead
the attention, step by step, in any succeeding consid-
eration of the same idea, we shall ever have it at com-
mand, and with a single glance of thought be able to
run over all its parts. I have therefore explained
here, at some length, the conduct of the mmd m
numbering ; it seeming to me the best model m this
kind,whether we consider the many advantages de-
rived from such an orderlv disposition of our ideas,
or the great art and skill displayed in binding thes6
idea$ together. This also is farther remarkable, m
the consideration of number, that from it chiefiy we
derive the notion we have of infinity ; it being appar-
ent, that, in adding number to number, there is no
end ; the possibility of doubling or increasing our
stock in any degree, rem>aining as obvious to the un-
derstanding, alter a great and continued run of pro-
gressions, as when ii ilrst began the computation.
Sec. VIII. The Consideration of Jvumber^ of great
Use in ascertaining our Ideas of Space and Duration,
If we nov/ turn our thoughts towards space and
duration, here too we shall find that we very seldom
arrive at clear and distinct ideas of either, but when
we introduce the consideration of num.ber. The m^ore
obvious and limited portions, it is true, easily slide
into the mind, in the natural way of perception ; but
it was the necessity of comparing these together, that
put us upon the contrivance of certain stated meas-
ures by which precisely to determine the quantity in
each. Thus, inches, feet, yards, miles, Sec. ascertain
our ideas of extension ; as minutes, hours, days,
years. Sec. measure the progress of duration. The
iesser parts, as Iving most open to the notice of the
understanding, and being more on a level with its
powers, are retained with tolerable exactness ; and
U DUNCAN'S ELEMENTS
the larger portions, when the number of repetitions
of which they are made up is kno\Mi, are thereby al-
so reduced into clear and determinate conceptions.
A foot, and yard, are measures easily comprehended
by the mind ; nor do v/e find any difficulty in con-
ceiving a mile, when we consider it as equal to a
certain number of yards. If we are stii] for increas-
ing the standard, w-e may take the semi-diameter of
the earth, and supposing it equal to 8000 miles, make
use of it as a measure by which to ascertain the dis-
tance of the sun or fixed stars. Just so it is in dura-
tion ; from hours we rise to days, months, and years ;
4)y these, repeated, and added together, we measure
.time past, or can run forward at pleasure into futuri-
ty, and that without any confusion or perplexity.
Sec. IX. — Without they are apt to degenerate into a
cov fused and irregtdar Heap.
It is however to number alone that we owe this
distinctness of perception, inasmuch as space and
tim.e, considered apart from the regular and orderly
repetition of miles or }^ears, leave no determinate im-
py^^ssions in the mind, by which to knov/ and distin-
guish their several portions. Ideas of either, thus
taken in at a venture, are a confused and irregular
heap, especially w'here we endeavour to enlarge and
Tna;3nify our views, and give full play to the powers
cf our intellect. Something indeed the mdnd con-
ceives, vast and mighty, but nothing that is precise,
accurate and just. But v,hen it begins to consider
tliese ideas as made up of parts, and fixing upon such
as are proportioned to its reach, sets itself to examine
Iiov/ often they are repeated to make up the v/hole,
the perceptions of the understanding put on a nev/
fcnn, a.nd discover their exact bounds and limits.
OF LOGIC. 45
Sec. 'yi.^Inf.nity an Object too mighty for the Sui-vey
of the Human Mind.
And thus, as before in number, so here in exten-
sion and duration, the mind begins \vith simple and
obvious notices, advancing by degrees to more en-
larged and intricate conceptions. A day, or a fur-
long, are of easy apprehension to the understanding,
and by their subdivisions into still lesser spaces, ex-
hibit themselves distinctly in all their parts. Vv^ith
these variously repeated, we travel through space and
time ; so that being able to reduce all our ideas of
this class, however mighty and enlarged, to the clear
and determinate perceptions of number, we can con*
duct our thoughts vrithout perplexity, and never fmd
ourselves puzzled, but vrhen, presuming too much on
our own strength, we launch into speculations, that
stretch beyond the powers cf the human, intellect. —
Number may be compared to a line, that, setting. out
from unity, runs on in a continued increase of length,
wit'iout a possibility of ever arriving at its ultimate
period. So far as we pursue it in our thoughts, and
trace its regular advances, so far our ideas are accu-
• rale and just. But when we let loose our under-
standings, alter a boundless remainder, and Vv'ould
fathom the depth of infinity, w^e find ourselves lost
amidst the greatness of ouro^^Ti conceptions. Some
notions, it is true, v/e have, but such as, exceeding
the dim.ensicns cf the mind, lie involved in darkness
and obscurity ; and being destitute of order, method,
and connexion, afford no foundation \\ hereon to build
ai?7 just and accurate conclusion.
Sec. XI. — Js^ever represented in it fi full Dimensions., but
by an endless and ever grooving Idea.
And this perhaps may be trie reason Avhy many
modern philosophers, m tiieir discourses concerning
/.
46- DUNCAN'S ELEMENTS -
infinity, have run into apparent contradictions ; be-
cause, encountering an object too large for the sur-
vey of the understanding, they found themselves sur-
rounded with inextricable difficulties, which their
scanty and defective ideas vrere by no means able to
dissipate or remove. The truth of it is, finite ideas
alone are proportioned to a finite understanding ; and
although we are not wholly without a notion of the
infinity of number, yet it is not such a one as com- -
prehends and exhausts its object, or exhibits it to the
mind in its full size and dimensions. We only see-
the idea, as capable of an endless increase, but cannot
by any effort of thought take in the whole prospect ;
and indeed it is properly that part of it which lies be--
yond the reach of our perception, and still remains. to
be taken into the account, to vrhich we give the name..,,
of infinity.
Sec. XII. — Duration^ "d'heth^T comidered as fiast or to
come. Boundless^ nvhence our Idea of lit emit y.
This idea of the infinity of number, imperfect as^
it may seem, is nevertheless that by which the mind
ascends to the conception of eterrdty and immensity.
For when we consider duration, either as past or to
com.e, we find nothing to stop the progress of our
thoughts, in the repetition of years, or millions of
years : the farther we proceed, the more the idea
grows upon us ; and when we have wearied ourselves
with vain efibrts, v/e must ovrn at last that we can no
more arrive at the end of duration, than at the end of
number. It is true, the several generations of men
rise and disappear in very quick successions ; earth it-
self may decay ; and those bright luminaries that
adorn the firmament of heaven, be eytinguished.
But the course of time will not be thereby disturbed ;
that fiows uniform and invariable, nor is bounded by
OF LOGIC. ^r
the period of their existence. This double view of
duration, as having ah^eady revolved through num-
berless ages, and yet still advancing into futurity in
an endless progression, properly constitutes our ideas
' of eternity. We speak indeed of an eternity past, an
! eternity to come, but both these are bounded at one
- extreme : the former terminates in the present mo-
Bient, and therefore has an end : the latter sets out
from the same period, and therefore has a beginning ;
■ but, taken together, they form a line both ways infi-
nitely extended, aiid which represents eternity in its
! full dimensions.
\ Sec. XIII. The Idea of Immeiidty derived from the
Condderation ofS/mce ex^er growing on all sides of us.
\ As, in the consideration of time, we fix upon the
I .present moment, regarding it as the middle point
which divides the Vvhoie line of duration into tvvo equal
\ parts ; so, in the consideration of space, that particu-
i lar place in which we exist is looked upon as a kind
' of centre to the whole expansion. From thence we
let loose our thoughts on every side— above, below,
around— and find we can travel on, in the repetition
I of miles, and millions of miles, without ever arriving
I at the end of the progression. It is not difficult, in-
deed, to carry our conceptions to the utmost bounds
of the universe ; at least so far as it falls within our
notice. But then the imagination rests not here ;_ it
I sees immieasurabie spaces beyond, capable of receiv-
I ing nevvT worlds, which it can pursue,^as rising one
! above another in endless succession. This consider-
ation of space ever growing on all sides of us, and yet
never to be exhausted, is that which gives us the idea
i of iminensity : which is in fact nothing else but the
infinity of number, applied to certain portions of ex-
tension, as miles, or leagues, Sec. and these conceived
48 [DUNCAN'S ELEMENTS
as extended every way around us, in infinite and in-
numerable right lines.
Sec. XIV. — Compound Ideas resulting from the Union
of Perceptions of different Kinds.
Hitherto we have considered the mind as employ-
ed about one and the same idea, enlarging and diver-
sifying it in various forms. We have seen it rising
from the most simple and obvious notices to the con-
ception of infinity itself; ana taken a view of it in all
the different stages of its improvement. Let .us now
proceed to the more complicated act of composition,
when the mind brings several ideas of diiferent kinds
together, and voluntarily combines them into one
complex conception. Such for instance, is our idea
of a tune., as com.prehending a variety of notes, with
m.any different modulations of sound. And here it
is to be observed, that though the complex idea may
be excited in us, by hearing the air itself struck off
upon a proper instrument ; yet, considered originally,
it still belongs to this class of perceptions, which are
distinguished as the arbitrary collections of the mind.^
It vras the musician, or composer, that combined the
several notes, and determined the order in which they
were to follov*" one another ; nor had t'nat peculiar
composition of sounds any real union in nature, be-
fore tiiey were tlius brought together in his mind.
Of the same nature are most of our ideas of .human
actions ; for though many of thcmx come to our no-
tice by seeing the actions themselves, or hearing them
described by others, as distilling^ cawitig^ treason.) &c.
yet it is plain that they must have been projected
and contrived in the m.ind of man before tiiey had a
real existence.
OF LOGIC. 4§
Sec. XV. — How the mind is determined in making these
Combinations.
It is here that the understanding has the greatest
scope, and finds most employment for its active pow-
ers : nor indeed is it possible to set any bounds to the
ideas of this class ; the combinations already made
being almost innumerable, and those yet in the pow-
er of the mind affording an endless diversity. It may
not, howevei> be amiss to consider how we conduct
ourselves amidst so great a variety, and by v/hat rules
we proceed in making those combinations to which
we have affixed particular nam.es, while others, per-
haps, no less obvious, are neglected. The idea of
killing, for instance, joined to that of a father, makes
a distinct species of action, kno%\^i by the name of
fiarricide. It was doubtless as obvious to. distinguish
between the killing of an old man and a child, vrhich
yet we find is not done ; both these actions being com-
prehended under the general name of murder. By
what views therefore does the mind regulate its com-
binations ? Why is it determined to one collection of
ideas rather than another ? This cannot be ■ well un-
derstood, without observing, that it is the end cf lan-
guage to comm.unicate our thoughts one to another.
V/ords are the siirns of our ideas, and serve to express
the conceptions of the mind. Now it is apparent, that
such conceptions as are most apt to occur in the com-
merce of life, would be first distinguished by particu-
lar nam^es ; the frequent occasion men have of men-
tioning these among themselves, rendering this abso-
lutely necessary. But as many of these conceptions
are collections of different simple ideas, hence we are
insensibly led to such peculiar combinations, as arc
most serviceable to purposes of mutual intercourse
iuid communicatiou,
G
5© DUNCAN^s ELEMENTS
^ec. X^T[. — Ideas of Human Jctions often formed^ be^
fore the Actions themselves exist.
Let us suppose, in the first beginnings of society*
a company of legislators met together, in order to con-
sult on proper regulations for the government of the
community. If they are men of prudence and fore-
sight, they will naturally observe many new occurren-
ces, likely to arise from this coalition of mankind, and
their living together in crov/ds. Perhaps the age in
which they live, has not produced an instance of one
man's killing another ; yet from the knowledge of
their ot\ti frame, and their power of doing hurt, they
conceive this as a possible case, and are willing to pro-
vide against it. Thus all the ideas that enter into the
complex one of murder, are brought together, and
united into one conception, before the action itself re-
ally exists. It is not, however, thought necessary to
take into consideration the age of the person ; the
chief thing in view being to prevent the putting an
end to another's life unjustly, whether old or young ;
and therefore the penalty equally effects both -cases.
But when they come to considerthe relation in which
the person killed may stand to the murderer, here
there appears a manifest difference ; ^s it adds to the
crime, when committed upon a beiy^factor, and ren-
ders it particularjy heinous in the case of a father. —
Tljs last, therefore, is made to constitute a distinct
species of iictiou, and has a peculiiir punishment allot-
ted to it. Thus we see how men, according to their
diiierent manner of life, and the relations they stand
in to one anr>ther, are naturally led to form sevei-al
collections of simple ideas, preferably to others, as
foreseeing they may have frequent occasion to take
notice of such precise combinations. And because it
would be tedious in conversation, every time the^e
OF LOGIC 51
complex notions occur, to enumerate all the ideas of
which they consist ; therefore, for the sake of ease and
dispatch, tliey give them particular names, and there-
by render the compositions- fixed and permanent.
Sec. XVII. — The necessity of Mutual Intercourse avd
MeJi's particular Aims in Life^agreat Source cfCom'
plex Ideas.
That it is in this manner "we come by our complex
ideas, which multiply upon us according as the exi-
gencies of society require, o/ our pursuits, method of
fife, and different aims, throw occasions in our way, of
combining such and such perceptions together, might
be easily made to appear, by a short view of the com-
binations themselves. Human actions, as oecurring-
most frequently, and affording large matter of con-
versation, debate, and inquiry among men, have been
Tery nicely modified, and distinguished into classes,
according to the several circumstances most likely to
attend them. In like manner, the arts and sciences,
in propoilion as they are eultivaeed, leading us into
many compound views of things, which otherv/ise-
would never offer themselves to the consideration of
the mind ; the complex ideas of this sort, with the
names by which they are expressed, are, we find, the
work of such paa-ticular nations, where these arts and
sciences have chieuy flourished. The Greeks, for
instance, excelled in learning and polite knowledge ;
hence many of the terms belonging to rhetoric, poe-
try, philosophy, physic, Sec. come originally from
their language. Modern fortification has received
its greatest improvements among the French; and
accordingly the ideas and terms of the art are mostly-
derived from writers of that nation. In Italy, archi-
tecture, music, and painting, have been the great ex-
ercise of the men of genius ; it is tlierefore amon^
52 DUNCAN'S ELEMENTS
them that we iind the several complex notions belong-
ing to these parts of study, as well as the names by
which they are expressed ; nor can w^e discourse ac-
curately and minutely of the above mentioned arts,
without having recourse to the language of that cli-
mate. And if we descend into the particular callings
and professions of men, they have all their peculiar
coilections of ideas, distinguished by their several
riames, and hardly known but to such as are conver-
ssant in that manner of life. Thus calcination, coho-
bation, filtration, Sec. are words standing for complex
ideas frequently framed in the minds of chymists, and
therefore familiar to men of that employment. Yet
as these, and such like combinations, seldom occur in
common life, the generality of mankind, we see, are
in a great measure unacquainted wiih them.
JSec. XVIII. — >Hence different Sets of them prevail in
different Countries : and Words in one JLanmuige
have none to answer them in another.
I might pursue these speculations farther, and*shovv
hov/ the several fashions, customs, and manners of one
nation, leading th'cm to form many complex notions
"Which come not so naturally in the way of another ;
different sets of ideas prevail in different countries,
and of course have names appropriated to them in the
language, to which there are no w^ordsthat ansv/er.in
another. The procedure and forms of our courts of
justice have introduced many terms into the English
law, which stand for collections of ideas framed among
no other people. Nor w^ould it be possible to render
these terms by ruiy single w^ords of another language ;
because, where ideas themselves prevail not, there are
'no names provided to express them. In this case,
therefore, it becomes necessary to use circumlocu-
tions, and enumerate the several ideas comprehended
OF LOGIC. 5e
ip the collection, if we would so express ourselves, as
to be understood in the language of other nations. —
Nay, even among tlie same people, the change of cus-
toms and opinions frequently brings new sets of ideas,
which, of course, must be'distinguished by particular
names ; while, at the same time, the notions of former
ages grow into disuse, and the words answering them
are wholly laid aside, or employed in a signification
different from what they had before.
Sec. XIX. — This, too, the cause that Languages arc
in a perfietual fiux .
Thus languages are in a perpetual fliix, and by de-
grees vary so much from their original frame, as to
become unintelligible even to the descendants of those
v/ho speak them. If we run back into the ages of
chivalry in England, when tiles and tournaments were
in fashion, how- m.any complex ideas, peculiar to that
mode of life, shall we find familiar among the men of
those times, v/hich are no'.v little known or attended
tor On the contrary, the improvements in arts and
sciences that have since taken place, have led us into
innum.erable ^ievrs of things, to which our fore-fath-
ers Vv' ere perfect strangers. Eut I shall not push these
refiections any farther, believing that what has been
said will be sufficient to show the origin and progress
cf cur compound ideas, and how the mind is directed
in the choice of the combinations it makes. Wc
therefore proceed to the consideration of abstract ideas^
which make the subject of the following article.
54 DUNCAN'S ELEMENTS
ART. II.
OF ABSTRACT OR UNIVERSAL IDEAS.
Sec. I. — General Ideas formed by the Abstraction of
the Mi7id.
H
AviNG dispatched what was necessary to be said-
concerning our compoundjdeas, considered merely as
they are combinations of the understanding, it is no^r
time to explain how we come by our general notions
which serve to represent to us a multitude of individ-
uals, and are the standards by v/hich we rank things
into sorts. And this, as we have before intimated, is
done by the abstraction of the raind ; which act may
be extended to all our ideas, whether simple, com-
pound, or of substances. If, for instance, we fix our
attention on any particular colour, a& scarlet, v/e can
leave out the consideration of all present circumstanc-
es, as the subject in which it inheres, the time and
place of seeing it, &c. and retaii:iing only the impres-
sion itself, make it a representative of that quality or
appearance, wherever we chance ta meet with it. It
is thus that abstract and universal ideas are framed ;
for the mind regarding only the scarlet colour, which
one day it observes perhaps in a piece of cloth, anoth-
er in a picture, and a third in the rainbow ; the ap-
pearance is conceived to be the same in all these ob-
jects, and therefore is called by the same name.
Sec. II, — AU the Perceptions of the Understanding
particular.
But to enter a little more closely into this matter^
and show that these our general- conceptions are the
mere creatures of the understanding, it may not be:
amiss to take notice, that all our perceptions of tilings.
OF LOGIC. 55
whether ^ve derive them from sensation or reflection,
are of their own nature particular, and represent to us
S single, determinate objects. ^Vhen we see a horse,
I for instance, in the fields, our idea is that of an indi-
j vidual. If we hear a sound, it is something particu-
i lar, and different from what vre hear at any other
i time. Every perception of the m^ind is distinct from
) every other perception ; nay, and every idea brought
into view by the imagination, as when we frame the
image of a lion standing before us, is still singular,
.and represents a single object.
Sec. III. — The Idea of the S/iccies rfpresents ivhat is
ccmimon to different Individuals .
But when we come to take a view of these several
"Daniculars, we readily observe among some of them
a resemblance ; and framing to ourselves an idea of
those things in which any of them are found to agree,
w^e thereby get a general notion, applicable to many
individuals. Thus horses are found to resemble one
another in shape, voice, and structure of parts. The
idea, which takes in only the particulars of this re-
. sem.blance, excluding what is peculiar to each single
' animal, becomes of course common to all creatures
■ -of that kind, and is therefore the representative of a
; "whole class of beings. Accordingly the name of that
general idea is given to every ar.imal in which that
shape, veice, and structure is found ; for the word
; horse, implying only these particulars, must belong
, to all ci^atures wherein they exist. This is the first
step or gradation in the forming of abstract notions,
when the mind confines itself to the consideration of
individuals, and fi'ames an idea that comprehends
such only under it. The rank or class of things an-
ivrering to this idea, is called species in the language
-of the schools. So a horse is a certain species of an-
S6 DUNCAN'S ELEMENTS
imals, an oak is a species of trees, and a square is a
species of four-sided figures.
Sec. IV .—The Idea of the GeJius represents vjhat ia
common to several Species.
When we have thus learned to rank individuals
into sorts and classes, according to the resemblance
found among them, the mind proceeds next to con-
sider the species themselves, and often in these too
observes a certain likeness. Whereupon, throv/ing
cut all those particulars v/herein the several species
are found to disagree, and retaining oniy such as are
common to them eJl, we thereby frame a stiJl more
general idea, comprehending under it a variety of
different species. Thus a sparrow, a hawk, and ea-
gle, Sec. are distinct species of birds, which have each
their peculiar shape and make. They nevertheless
resemble one another, in being covered with feath-
er.s, and provided with wings that bear them through
the air. Out of these particulars we form a new
idea, including all the common properties of the feath-
ered kind ; and appropriating to it the name of birdy
mark by that word another class of things, of a high-
er order than any of the former. This superior -di-
vision, which extends to several species at once, is
called in the schools the genus., and is the second step
the mind takes in advancing to universal notions.
Sec. V. — The Mind may advance by manifold Grada-
tionsy in rising from Particulars to Generals.
And thus have I given a short, but I hope intelli-
gible account, of the business of genera and species^
about which so much has been said in the writings of
lop;ician5. Species, in strictness and propriety of
speech, is such a rank or class of things, as compre-
hends under it only individuals : genm advances stilt
OF LOGIC. 57
higher, and takes in a variety of distinct species. It
is, however, to be observed, that the mind in rising
from particulars to generals, does not confine itself
to one or two gradations, but may carry its views
through the whole extent of things, until at length it
arrive at an idea embracing the universal compass of
nature. For when vre have ranked tilings ;nto scriis,
and reduced these again to tiie higher order or jy-.-jz-*,
these ^fwera are still found to resemble one anotiier in
some particulars, Avhich being collected into one '.dca,
form a neAv and more comprehensive division of thinpjs.
Thus bird is a genun^ embracing all the varieties of
the feathered kind. Fish implies the several species
of living creatures v/hich inhabit the waters. Quad-
jufied and insect are also universal ideas, that take in
many inferior distributions and classes. Yet all these
different orders of being, have this in common, that
they are provided v.ith organical bodies, fitted for the
purposes of life and spontaneous motion. An idea,
tlierefore, comprehending only these last particulars,
will equally belong to all the divisions before enumer-
ated ; and the v, ord cmimal, by which it is expressed,
becomes a general name for the several creatures en-
dued with life, sense, and spontaneous motion. If we
are for carrying our views still farther, and framing
a yet more universal notion, Vv-e can cast cur eyes upon
both the animate and inanimate parts of nature ; where-
in we fmd this mutual correspondence, that they ex-
ist, and continue in being. This last idea, therefore,
of being in geneml, comprehends under it all the vari-
eties of things, and may be universally applied to
whatever has life or existence ; so that in respect of
the present frame of nature, it is the highest and most
universal idea vre have.
H
58 DUNCAN'S ELEMENTS
VI. — Whence many intermediate Steps beiweeii the
highest Genus and lowest S/idcies.
In this series of notions, rising one above another,
in the degree of universality ; that division, vvhich
comprehends under its several genera, is called in the
schools the higher genus ; which denomination con-
tinues, until we arrive at the last advance of the un-
derstanding, when, being come to the most general of
all ideas, that admits not of a superior, it is distin-
guished by the name of genus generalissimmn. In like
manner the several genera^ comprehended under a
higher ge-nus^ are, in respect of it, considered as spc-
dss ; and as these two last have species under them,
the inferior divisions are, for distinction's sake, term-
ed lower species. Thus the prcgrcssion continues, and
when v/e come to the iov/est subdivision of all, com-
prehending only individuals, which, as I have before
iiitimated, constitutes the proper species, this the
schools denominate the species spe&ialissijna. All that
lie betYv'een it and the highest distribution of things,
are the intermediate genera and species, which are
termed, each in their turn, genus generaiius, or species
ipecialior, according as we consider them in the as-
cending or descending scale of our ideas ; or, to speak
in the language of logicians, according to their ascent
or descent, in linea praclicajnentali. I should not Iiave
entered so far into these verbal disquisitions, had not
the terms here explained, been such as frequently oc-
cur in the vvriti'ngs of philosophers ; insomuch, that
v/ithout some knowledge of them, we must often be
at a loss, in the pi'osecution of these studies. Besides,
it is both curious and uselul, to see the gradual pro-
gress of the mind, in its advances from paiticular to
general conceptions — to observe it ranging its ideas
into classes, and establishing a just and regular sub-
OF LOGIC. 59
ordination in its views and notices of things. This
is the shortest way to knowledge, and aubrds the best
lueans of preserving the order and due connexion of
cur thoughts, so as to make them subservient to the
increase of science. For when we see how things
comprehend, or are comprehended in, one another,
we are able to discover the mutual dependence of all
the several branches of knowledge Avhich leads us into
the true and natural method of conducting our under-
standings in tlie search of truth.
Sec. VII. — General Ideas the Creatures of tht Under'-
standing.
From what has been said, it is evident, that general
ideas are the creatures and inventions of the under-
standing. Nature, it is true, in the production of
things, makes many of them alike : but it is the mind
alone, that collects the particulars in which they agree,
into one idea, and sets it up as a representative of ma-
ny individuals. And nov/ I think. we may venture
upon that much-agitated question, where do the gen-
era and species of things exist ? To which I answer,
in the mind. Universality belongs not to things them.-
selves, it being apparent, that they are all particular
m tlieir existence. Ilcv/ever, as they often have ma-
ny properties in common, the understanding, by unit-
ing these into one conception, obtains a general idea,
under which it ranks all the several objects v/herein
these properties are found. So far indeed we must
allow, th.at the particular combination of properties,
which constitutes the genus or species, exists in all
the individuals referred to that genus or species ; but
then it is in conjunction with other properties, by
which these individuals are distinguished from one an^
other. Thus the collection of simple ideas, signified
by the word bird^ is to be found, for instance, in a
CO DUNCAN'S ELEMEInTS
/larj/:, cr any other single animal, to ^vhich we applji'
that general name : but the notion itself, abstracted
from all the particulars to v»'hich it belongs, has evi-
clenily no existence out of the understanding. There
is not a being in nature that can be called a bi7^d in
general, or that does not necessarily imply, in the very
conception of it, several simple ideas, besides those
marked by tliat vv^ord. For the name, in this case,
signities no more than an anirnal covered with feath-
ers, and provided v/ith wings, without regard either
to shape, bulk, or the particular time and place of its
er.istence. These last considerations, hov/ever, are
inseparable from the reality of things, and therefore
must be added to the general idea, before we can con-
ceive any thing conformable to it actually brought into
being.
Sec. VIII. — Co7ir.idered ajiart^ they exist only in the
Mind^ but in co'rijunction ivith other Ideas in the in-
divldiials cornnttiiended under theryj.
Hence we see at once, vviiat sort of an existence gen-
eral natures have. Considered apart, and by them-
fselves, they are v»'hoIIy the workmanship of the un-
derstanding, and derive their being and reality from
it ; but viewed in conjunction with other ideas that
co-exist v.dth them in the several objects of nature,
they are to be found in the individuals to which they
refer ; and therefore, according to tliis way of concep-
tion, may be saitl to have an existence in them. Thus,
so long as t]ie ideas ansv/ering to the words irecin or
tree^ coutinue general and undetermined, they have no
real objects answering them in nature ; nor can tlie
collections of simple ideas, marked by these names,
while ail others are supposed excluded, exist any
•vhere out of the understanding. Nevertheless, as ali
4he simple ideas, included in the general notion of
OF LOGIC. 6b
man^ are to be found in every particular man — and all
those implied in tne notion of a tree^ in eveiy particu-
lar tree — iience the general nature of ma7i^ exists in
every individual rnan^ as does the general nature of a
t)'€s^ in every individual tree^
Sec. IX. — Differe~iice cf Ideas considered as compound
and as universal.
One thing still remains to be observed, with regard
to these our general ideas ; that, though many of them-
are evidently combinaiionB of different simple ideas,
and according to Ihat way of considering tliem., are ,
included in the first division of our complex concep-
tions, those, namely, framed by the composition of the
mind ; .yet Vr^e are carefully to distinguish between an
idea, as it is compound, and as it is universal. In the-
first case, the mind chiefly considers the several ideas'
that are combined together ; or, in other words, all
the attributes, qualities or parts, that are contained in-
any idea. Thus the idea of a bird^ includes life, sense,
spontaneous m.otion, a covering of feathers, wings,
kc. none of which can be left out v, ithout destroying
the very nature of the idea, and niaking it something-
quite diiFerent from what it v/as before. This way"
of considering things according to the nun^ber of their
parts and propertiec, is called by logicians the com-'
Jirehension of an idea. But the uni-versality of our
notions imiplies quite another turn of thinking, in as
much as it fixes the regard of the m^ind, upon the-
subject to v/hich our ideas extend, or the mdividuals
and species, comprehended under them. In this sense,
the idea ansv\^ering to the word bird^ takes in the sev-
eral species of the feathered creation, the ha^iuk^ the
eagle ^ sharroiv^ lark^ and. innumerable others, to all
which it may, with equal propriety, be applied. And
here it is remarkable, that the idea loses nothing Oi
62 DUNCAN'S ELEMENTS
its force or comprekendon^ by being restricted to a par-
ticular kind, When I say the bird of Jove^ thoiigh
in this case the idea is restrained to the eagle alone, it
still remains as distinct, and includes as many simple
ideas in its composition, as when, before, it was ex-
tended to ail the different tribes of feathered animals.
Sec. X. — The coinprehcndon a?icl extension of our Ideas.
We see, therefore, that our com.pound ideas may
continue the same in respect of their attributes, or the
number of parts, and yet vary considerably in the de-
gree of universality. The general ideaof ?/?fm is the
same, whether applied to the whole human race, or
those of any particular nation. When I affirm, for
instance, of mankind in general, that their knov/ledge
falls short of perfection, and afterv/ards make the like
observation of the men of the present age ; in both
cases, the word man stands for one and the same col-
lection of simple ideas ; but in respect of the individu*
als to which it is applied, there is a great and manifest
difference. That is, the tel'm inan^ denotes one in-
variable com.pound idea ; v/hich, notv/ithstanding,
considered as a general notion, may be contracted or
enlarged at pleasure. And as in the former case, the
several parts of the compound idea are called its com-
prehendon ; so in the latter, the individuals, to which
the universal idea is applied, are called its extension,
I might add miany more observations on this subject,
but choose rather to stop here, having said enough to
explain. the difference between compound and abstract
ideas, and show the reason of my ranging thern un-
der distinct heads.
OF LOGIC. €3
ART. III.
CF OUR IDEAS OF RELATIONS.
Sec. I. — 'Ideas of Relations exceeding numerous.
1 coM^ nov7 to the third and last division of those
ideas, which I consider as the creatures and work-
manship of the understanding ; such, namely, as arise
from the comparing of things one with another. For
the mind, in its views, is not tied to single objects ;
but can examine their references and respects, in re-
gard to others, brought under consideration at the same
time. And when it does so, and thence derives new
notices of things, tlie ideas thus got are called rela-
tions, and make, I am apt to think, the largest class
of all our perceptions. For every single object Vv-iil
admit of almost innumerable comparisons with oth-
ers, and in this sense may become a very plentiful
source of ideas to the understanding. Thus, if we
compare one thing vdth another, in respect of bulk^
we get the ideas oi greater^ less, or equality ; if in re-
spect of time, of older and younger ; and so for ether
relations,- which we can pursue at pleasure, almost
v.'ithout end ; whence it is easy to conceive, how very
extensive this tribe of our perceptions must be.
Sec. II. — Men. chiefly determined to particular CoTiipar-
ir,ons by the Wants and Exigences of Life,
I shall not pretend to trace out these ideas particu-
larly, nor indeed so much as to enumerate their sev-
eral divisions ; it being enough to observe, that here,
as well as in the other kinds of our -complex ideas,
Ave bound ourselves, for the most part, to such com-
parisons, as tlie exigences of society, the v/ants of life,*
and the different professions of men, render neces-
sary ; and are more or less accurc^te in tracing out
64 DUNCAN'S ELEMENTS
the relations of things, according to the degree cf im-
portance they appear to have in these respects. The
relations of men one to another, arising either from
the ties of biood, their several ranks and places in the
communitv, or a mutual intercourse of good cfiices,
being of great A\'sight and concern in the commerce
of life, have in a particular manner engaged our at-
tention, and are therefore very minutely described. —
For the sam^e reason, men have found it necessary, to
determine, as exactly as possible, the various depend-
ence of things, as their happiness is nearly connected
v.ith this knowledge. When vre consider objects
raerely in respect of existence, as either giving or re-
ceiving it, we come by the ideas of cause and effect :
nor need I mention how much the welfare of man-
kind depends on an extensive view of things, as they
stand connected in this relation; it being evident, that
-the several schemes and purposes of life, are all con-
ducted upon a previous supposition, that certain knov.n
causes wUl have their usual regular effects, and such
and such actions be attended v\'ith such and such con-
sequences.
Sec. III. — -Relaticns cf Creator cyid Creaturey'Cfc.
But there are other relations of this kind, besides
those that regard mjerely existence ; as when we also
take into the account the additional gifts of a capacity
for happiness, and the mea.Ds of attaining it ; which
constitutes the relation oi Creator and creature^ m the
more solemn accepteition of these v/ords. Again, when
v/e consider the great Author of our being, not only
as the Creator of -the universe, but also as preserving
r.nd holding it together, and presidintj over the present
name of things with uncontrouled dominion ; he then
appears under the notion of a vioral Governor^ to whom
-ive arc accountable fcr cui' act:cn3, and the use we
OF LOGIC. 65
make of those powers and faculties we derive from
]>im. Now as it is of the highest consequence for
men, not to be unacquainted with these, and such like
relations ; hence we find, tliat the wisest nations, and
such as best understood the true application of tlie
powers of the mind, have always made it their chief
♦otudy to regulate and ascerLain these ideas, and trace
them in all their consequences. And thus we may,
in some measure, perceive how the mind proceeds in
comoarihg its ideas together, and by what views it is
chiefly governed, in framing the complex notions of
this class, by which it represents the various habitndes
of things, I shall only add upon this subject, these
two observations.
Sec. I v. — Our Ideas of relations very dear and distinct.
First, that our ideas of relations, are for the most
part very clear and distinct. For the compelling of
tilings together, being a voluntary act of the mind,
Vv-e cannot but suppose that it must be acquainted wiih
its o^^^l \-iews in the comparison ; and of course have
a clear conception of the foundation of that relation,
it sets itself to enquire into. Thus the relation of
cause and effect, implying only that one thing produc-
es, or is produced by another, which notions are al-
ways distinctly settled in the understanding before it
goes about to m.ake the comparison ; it is evident, that
the idea representing this mutual respect of objects,
will be no less clear, than are the notions themselves
upon which the relation is founded. And what is still
more remarkable of the ideas of this class ; they cease
not to be distinct, even where the subjects compared
are but very imperfectly knovrn. For I can well
enough conceive, that one thing has produced anoth-
er, and that therefore they stand related as cause and
effect, though my ideas of the things themselves may
I
66 DUNCAN'S ELEMENTS
perhaps be very obscure, and come far short of repre-
senting their real nature and properties. I doubt not
but it will be readily owned, that our idea of the uni-
verse, considered as comprehending the whole frame
of created things, is very inadequate ; and I think it
is still more apparent, that our notion of the Supreme
Being comes not up to the excellence and perfection
of his nature. Yet we very v/ell understand what is
meant by calling God the Author of the Avorld ; and
though we comprehend not the manner of his produc-
ing it, find no difficulty in framing the ideas, the rela-
tive words Creator and creature stand for
Sec. V. — Ideas of Relatians among the most imfiortant
Conceptions of the Mind.
I have yet another observation to make upon this
subject ; and it is, that our ideas of relations are
among the most important conceptions of the under-
standing, and afford the largest field for the exercise
and improvement of human knowledge. Most of
our enquiries regard relative ideas, and are set on
foot with a view to investigate the mutual habitudes
of things. The mathematician has taken quantity
for his province, and teaches us how to compare mag-
nitudes of diiterent figures a.nd dimensions, in order
to judge with certainty of their relative properties.
The philosopher attaches himself to the chain of caus-
es and effects, and endeavours to trace out the various
dependence of things considered in this light. In fine,
whither do all our researches tend, but by means of
certain known properties and relations, to find out
others that stand some hovv" connected vv^ith them ? As
for the importance of these conceptions, no one can call
that in qu'^stion, who reflects ; that from our relations
to our Creator and one another, arise all the duties of
mcrulity and religion, and that the correspondence of
OF LOGIC. 67
the several objects of nature, to the organs of the body,
and faculties of the mind, is that by which alone we
can judge of what ^^dll procure us happiness or mis-
ery. Whence it is evident, that without an exact
knowledge of these relations, M^e must wander on in
life with great uncertainty, and may often plunge into
calamities and misfortunes, by those very pursuits
from which we expected nothing butjoy and pleasure.
Sec. VI. — Recapitulation.
Thus have I gone through the several divisions of
our ideas, which I have endeavoured to represent in
such a manner as their vast extent may most easily
appear, and the conduct of the mind in framing them
be distinctly apprehended. I might easily run into
other distinctions, by considering thein as clear or
obscure, adequate or inadequate, true or false. But
the limits of this tract will not allow my entering
more fully into the subject, and I think it the less
needful, because the very names are almost sufficient
to convey a notion of these several kinds of ideas into
the mind. But as the division explained above seems
to be of great importance, towards settling in the un-
derstanding a just view of the progress of human
knowledge, and the steps by which it advances from
one degree of improvement to another, I shall here
run over it again in as few words as possible, that the
whole process may be seen at once. Our ideas are
all derived into the understanding, either by sensation
or reflexion. This, however, is observable, that one
and the same object often excites a variety of percep-
tions at once, which are nevertheless readily- distin-
guished by the mind, and appear each under a form
peculiar to itself. These constitute our primary and
original notices, and are easily kno^vn from all others,
in as much as they are entirely void of plurality, and
63 DUNCAN'S ELEMEN^TS
cannot be dhided into two or more different ideas.
They are also the materials out of which the others
are formed, and are therefore, by way of distiction,
called simple ideas. But the mind, though it has no
power over these, either to fashion or destroy them,
can yet combine them in an inhnite number of Avays ;
and from their various combinations result ail our com-
plex ideas, which are of two principal kinds. First,
such as are derived from without, ajid represent these
combniations of simple ideas, that have a real exis-
tence in nature. Of this sort are ail our ideas of sub-
stances. Secondly, the conceptions formed by the
mind itself, arbitrarily uniting and putting together its
ideas. And as this makes by far the largest class, and
comprehends all those ideas v/hich may be properly
termed our o^vn, as being the real workmanship of the
understanding ; so they fall very naturally under three
distinct heads. For either the mind combines sever-
al simple ideas together, in order to form them into
one conception, in which the number and quality of
the ideas united, are principally considered ; and
thus it is we come by all our compound notions : cr
it fixes upon any of its ideas, whether simple, com-
pound, or of substances ; and, leaving out the circum-
stances of time, place, real existence, and whatever
renders it particular, considers the appearance alone,
and makes that a representative of all of the kind ;
whence our abstract and universal ideas are derived :
or lastly, it compares things one with another^ exam-
ines their mutual connexions, and thereby furnishes
itself with a new set of notions, knov/n by the name
of relations, which, as has been already remarked,
.make by no means the least important class of our
perceptions. This division of our ideas, as it seems
lobe the most natural, and truly to represent the man-
ner m v/hich thev are introduced into the mind, so I
OF LOGIC. 63
believe it will be found to comprelvc:^d them in c!i
their varieties. I shaii therefore now proceed to offer
some observations upon language, c.s being the grtut
instioinient, by which we are ei liable d to iiiuke our
ideas and perceptions knowTi to oihers.
CHAP. V.
OF WORDS, CONSIDERED AS THE SIGN OF OUR IDEAS.
Sec. I. — IFords furnish the I^teans cf recording our
oim Thoughts.
W E have seen hew the ir^ind comes to be first fur-
niched with ideas, and by what metriods it contrives to
diversify and enlarge its stock : let us now consider
the means of maldng kno-(,vn cur thoughts to ethers,
that we may not only understand how knowledge is
acquired, but also in what manner it may ])e commu-
nicated with the greatest certainty and advantage.
For our ideas, thcugn manifDld and various, are nev-
ertheless, all within cur own breasts, invissible to oth-
ers, nor can of themselves be mude to appear. But
God designing us for society, and to have a fellowship
wuth those of our kind, has provided us with organs
fitted to frame crrticulate sounds, and given us also a
capacity of using those sounds as signs of internal
conceptions. Hence spring words and languages ;
for ha^'ing once pitched upon any sound, to stand as
the mark of an idea in the mind, custom, by degrees,
establishes such a connexion between them, that the
appearance of the idea in the understanding always
brings to our remembrance the sound oi* name by
which it is expressed ; as, in like manner, the hear-
ing of tiiC sound never iails to excite the idea for
70 DUNCAN'S ELEMENTS
which it is made to stand. And thus it is easy to con-
ceive, how a man may record his own thoughts, and
bring them again into view, in any succeeding period
of life. For this connexion being once settled, as the
same sounds will always serve to excite the same
ideas : if he can but contrive to register his words, in
the order and disposition in which the present train
of his thoughts presents them to his imagination ; it
is evident he will be able to recall these thoughts at
pleasure, and that too in the very manner of their first
appearance. Accordingly we find, that the inven-
tions of writing and painting, by enabling us to fix
and perpetuate such perishable things as sounds,
have also furnished us with the means of giving a
kind of permanency to the transactions of the mind,
insomuch that they may be in the same manner sub-
jected to our review, as any the other abiding objects
of nature.
Sec. II. — And of the mutual Communication of Knowl-
edge from one Man to another.
But besides the ability of recording our ovni thoughts
there is this farther advantage in the use of external
signs, that they enable us to communicate our senti-
ments to otiiers, and also receive information of what
passes in their breasts. For any number of men,
having agreed to establish the same sounds as signs
of the same ideas, it is apparent, that the repetition of
these sovmds must excite the like perceptions in each,
and create a perfect correspondence of thoughts.—
When, for instance, any train of ideas succeed one
another in my mind, if the names, by which I am
wont to express them, have been annexed by those
with whom I converse, to the very same set of ideas,
nothing is more evident, than that by repeating those
names, according to the tenor of my present concep-
OF LOGIC. n
lions, I shall raise in their minds the same course of
thought as has taken possession ofmyo-v^m. Hence,
by barely attending to what passes within themselves,
they will also become acquainted with the ideas in
my own understanding, and have them in a manner
laid before their view. So that we here clearly per-
ceive, how a man may communicate his sentiments,
knowledge, and discoveries toothers, if the language
in which he converses, be extensive enough to mark
all the ideas and transactions of his n-iind. But as this
is not always the case, and men are often obliged to
invent terms of their own, to express new views and
conceptions of things ; it may be asked, how, in these
circumstances, we can become acquainted with the
thoughts of another, when he makes use of vrords to
which we have never aimexed any ideas, and which
of course, can raise no perceptions in our minds ?
.Now, in order to unveil this mystery, and give some
little insight into the foundation, growth, and improve-
ment of language, the foUovving observations will, I
am apt to think, be found of considerable moment.
Sec. III. — Simple Ideas cannot be conveyed into the
Mind^ by Words, or a Description ;
First, that no Vv^ord can be to any man the sign of
an idea, till that idea combes to have a real existence
in his mind. For names being only so far intelligi-
ble, as they denote knovai internal conceptions, where
they have none such to answer them, there they are
plainly sounds without signification, and of course
convey no instruction or knowledge. But no sooner
are the ideas to which they belong raised in the un-
derstanding, than, finding it easy to connect them
with the established names, we can join in any agree-
ment of ihis kind made by others, and thereby enjoy
the benefit made by their discoveries. The first thing,
/
72 DUNCAN'S ELEMENTS
therefore, to be considered, is, how these ideas may-
be conveyed into the mind ; that, being there, we may
learn to connect them with their appropriated sounds,
ar.d 30 becorae capable of understanding others, v.'hen
liicy Hiake use of these sounds in laying open and
CGinriunicating their thoughts. Now to comprehend
t'-ls distinctly, it will be necessary to call to niind, the
before mentioned division of our ideas into simple
ajid complex. And first, as for our sim^ple ideas, it
]iis been already observed, that they can find no sd-
it.il -sion into the mind, but by two original fount? ins
of lu'iow ledge, sensation and reflexion. If therefore
any of these have as yet no being in the understand-
ing, it is impossible by words, or a description, to ex-
cite thcni there. A m.an, who had never felt the im-
pression of heat, could not be brought to comxprehend
tiiat sensation, by any thing we might say to e^rplain
it. If we would really produce the idea in him, it
must be by applying the proper object to his senses,
andbringhig him within the influence of a hot body.
AVhen tiiis is done, and experience has taught him
the perception to which men have annexed the name,
hi'at^ it then becomes to him the sign of that idea ;
and he tiiencefoith understands the meaning of a term,
which, before, all the words in the world would not
liave been sufficient to convey into his mind. The
case is the same in respect of light and colours. A
man born blind, and thereby deprived of the only con-
veyance for the ideas of tiiis class, can neverbe brought
to understand the names by which they are expressed.
The reason is plain ; they stand for ideas that have
no existence in his mind ; and as the organ appropri-
£.ted to their reception is v/anting, all other contri-
yances are \ain,i;or can they, by any force of descrip-
tion, be itiised in his imagination. But it is quite
otiicrwise in our complex notion. For these being
OF LOGIC. 72
no more than certain combinations of simple ideas
put together in various forms — .if the original ideas,
out of which these collections are made, have already
got admission into the understanding, and the names
serving to express them are known — it will be easy,
by emmierating the several ideas concerned in the
composition, and marking the order and manner in
which they are united, to raise any complex concep-
tion in the mind. Thus the idea answering to the
word rahidow, may be readily excited iu the imagina-
tion of another, who has never seen the appearance
itself, by barely describing, the figure, largeness, po-
sition, and order of colours ; if we suppose these sev-
eral simple ideas, with their names, suiiaciently known
to him.
Sec. IV. — T/ie Aaiure of Complex Ideas Drfjiablc,
those of Simple Ideas not.
And this naturally leads me to a second observa-
tion upon this subject, namely : that words standing
for complex ideas are all definable; but those, by
v.diich ve denote simple ideas, are not. For the per-
ceptions of this latter class, having no other entrance
into the mind, than by sensation or reflection ; can
only be acquired by experience from, the several ob-
jects of nature, proper to produce those perceptions
in us. Words, indeed, may very well serve to remind
us of them, if they have already found admission in-
to the understanding, and their connexion with the es-
tablished names is knovvm ; but they can never give
them their original being and existence there. And
hence it is, that when any one asks the meaning of a
word denoting a simple idea, we pretend not to ex-
plain it to him by a definition, wtW knowing that to be
impossible ; but supposing him already acquainted
with the idea, and only ignorant of the name by which
K
74> DUNCAN'S ELEMENTS
it is called, we either mention it to him by some oth-
er name, with which we presume he knows its con-
nexion, or appeal to the object where the idea itself
is found. Thus, was any one to ask the meaning of
the word white, we should tell him it stood for the idea
as albus, in Latin, or blanc, in French ; or, if we tho't
him a stranger to these languages, might appeal to
an object producing the idea, by saying, it denoted
the colour we observe in snonv or milk. But this is
by no mea-ns a definition of the word, exciting a new
idea in his understanding ; but merely a contrivance
to remind him of a known idea, and teach him its
connexion v/ith the established name. For if the
idea after which he inquires, has never yet been rais-
ed in his mind — as suppose one, who had seen no
other colours than black and ivhite, should ask the
meaning of the word scarlet — it is easy to perceive,
that it would be no more possible to make him com-
prehend it by woitIs, or a definition, than to inculcate
the same perception into the imagination of a man
bor» blind. The only method in this case, is, to pre-
sent some object, by looking at which the perception
itself may be excited ; and thus he will learn both
the name and the idea together.
Sec. V. — 'Experience and Observation bring Men to an
Agreement in the JVames of Simple Ideas.
Should any one's curiosity now prompt him to en-
quire, how it comes to pass, that men agree in their
names of the simple ideas, seeing they cannot view
the perceptions in one another's minds, nor make
known these perceptions by words to others ; I an-
swer, that the effect here mentioned is produced by
experience and observation. Thus, finding, for in-
stanae, that the name, heat, is annexed to that impres-
sion which men feel when they approach the fire, I
OF LOGIC. rs
make it also the sign of the idea excited in me by such
an approach, nor have any doubt, but it denotes the
same perception in my mind as in their's. For we
are naturally led to imagine, that the same objects
operate alike upon the organs of the human body, and
produce an uniformity of sensations. No man fancies,
that the idea raised in him by the taste of sug-ar, and
which he calls sweetness, differs from that excited in
another by the like means ; or that ivormivaod, to v/hose
relish he has given the epithet bitter, produces in oth-
ers the sensation which he denotes by the word snveet.
Presuming, therefore, upon the conformity of percep-
tions, when they arise from the same objects, we easi-
ly agree as to the names of our simple ideas ; and if
at any tim^, by a more narrow scrutiny into things,
new ideas of this class come in our wa.y, which we
choose to express by terms of our own irrv^ention ;
these names are explained not by a ueFinition, but by
referring to the objects, whence the ideas themselves
may be obtained.
Sec. VL — The Co-nveyance of Complex Ideas by Deji-
nitions, a wise Contrivance in JSTature ;
Being in this manner furnished with simple ideas,
and the names by which they are expressed, the mean-
ing of terms that stand for complex ideas is easily at-
tained ; because the ideas themselves answering to
these terms, may be conveyed into the mind by defi-
nitions. For our complex notions, as v/as already ob-
served, are only certain combinations of simple ideas.
When, therefore, these are enumerated, and the man-
ner in which they are united into one conception ex-
plained, nothing more is wanting to raise that concep-
tion in the understanding ; and thus the term denoting
it comes of course to be understood. And here it is
worth while to reflect a little upon the wise contrivance
76 DUNCAN'S ELEMENTS
of nature, in thus furnishmg us with the very aptest
Tiieans of communicating our thoughts. I or were
it not so ordered, that we could thus convey our com-
■ple:: ideas from one to another by definitions, it v/ould
in many cases be impossible to make them known at
all. This is apparent in those ideas which are the
proper work of the mind. For as they exist only in
tlie understanding, and have no real objects in nature,
in conformity to which they are framed — rif we couid
not make them knov/n by a description, they must
lie forever hidden within our ov/n breasts, and be con-
fined to the narrow acquaintance of a single mind.
.\11 the fine scenes, that rise from time to time in the
poet's fancy, and, by his lively painting, give such
entertainment to his readers — were he destitute of
this faculty, of laying them open to the view of oth-
ers by words and descriptions — could not extend their
iniiuence beyond his own imagination, or give joy to •
any but the original inventor.
*^tc.\Yl.—r And of great avail towards the Imjirove-
ment aj Knowledge.
There is this farther a-dvantage in the ability we
enjoy, of communicating our complex notions by de-
finitions ; that as these make by far the largest class
of our ideas, and most frequently occur in the pro-
^;ress and improvement of knowledge ; so they are
by this m.eans imparted with the greatest readiness,
than which nothing could tend more to the increase
and spreading of science. For a dehnity is soon pe-
rused, and if the terms of it are v/ell understood, the
idea its:;lf finds a^n easy a-dmission into the mind.
Whereas in sim.ple perceptions, where v/e are refer-
red to the objects producing them, if these cannot be
come at, as is sometimes the case, the names, by
which they are expressed must remain empty sounds.
OF LOGIC. 77
But new ideas of this class occurring very rarely in
the sciences, they seldom create any great obstruc-
tion. It is otherwise v/ith our complex notions ; for
every step we take, leading us into new combinations
and views of things, it becomes hecessary to explain
these to others, before they can be made acquainted
with our discoveries^ And as the manner of defini-
tions is easy, requiring no apparatus but that of
words, which are always ready, and at hand ; hence
v.e can, with the less diincuity, rem.ove such obsta-
cles, as might arise from terms of our own invention,
v.^hen they are made to stand for nev/ complex ideas,
suggested to the mind by some present train of thhik-
ing. And thus at last we are let into the mystery
hinted at in the beginning of this chapter, -viz. how
we may beccine acquainted with the tlioughts of an-
other, when he. makes use of words to which we have
as yet joined no ideas. The answer is obvious, from
Vvhat has been already said. If the terms denote
simple perceptions, he must refer us to those objects
of nature, whence the perceptions them.selves are to
b^ obtained ; but if they stand for complex ideas,
their meaning may be explained by a definition. As
for the names of sim.ple ideas, I shall here dismiss
them ; it being sumcient to take notice, that our
knov/ledge this way can be extended -^only by experi-
ence and observation. But the theory of definitions
making a material pai^ of logic, and being indeed of
great importance tovrards the improvement of human
knovv'ledge, it wiii be necessary to lay it a little more
t>pen to the view of the reader.
Sec. VIII. — TAe Compositioii and Resclution of our
Com f ilex Ideas.
Complex ideas are, as has been already said, no
other tlian simple ideas put together in various forms.
78 DUNCAN'S ELEMENTS
But then it is to be observed, that in making these
collections, the mind is not always tied down to the
immediate view of tne simple perceptions out of
which they are framed. For if we suppose the un-^
derstanding already furnished with a considerable
stock of compound notions, these again may be made
the constituent parts of others still more compound-
ed, insomuch that the new idea thence arising may
be termed a combination of complex conceptions.
Thus the idea annexed to the word animal, includes
many perceptions under it, as life, sense, spontaneous
motion, Sec. In the like manner by the terai ration-
al, we denote a variety of simple ideas. If now com-
bining these two conceptions together, we form the
still more complex notion of a rational animal ; the
idea thus got is truly a collection of compound no-
tices. In a word, the same thing happens here as in
numbers, which we may consider not only as various
collections of units, these being indeed their original
and constituent parts ; but also as sometimes com-
posed of other lesser numbers, which, all put togeth-
er, make up the respective sums. Now in tracing
any very large number, when, for the ease of the
mind, we consider it at first as composed of various
others still less — if we next take these less parts to
pieces, and pursue them continually, untii-we arrive
^ the units cut of which they are composed; we
thereby totally unravel the collection, and being able
to push our researches no farther, rest satisfied in
the view thus offered to the understanding. Just so
it is in the examinslion of our complex ideas. For
■when any very compounded notion comes under the
inspection of the mind, in omer to be traced to its
first principles — we begin with resolving it into oth-
er ideas less complicated ; and taking these again to
pieces, one by one, still go on v/ith the search, until
OF LOGIC. rg
we have broken the v/hole into our first and simple
perceptions, beyond which the pursuit cannot possi-
bly be carried. And this is the reason why I have
all along called our simple ideas the foundation and
ground- work of human knowledge ; because, in un-
ravelling the conceptions of the mind, we find our-
selves at length bounded by these ideas, which are
indeed the last resort of the understanding.
Sec. IX. — The Karnes of Simfde Ideas may be consid'
ered as the Elementary Parts of Language.
From what has been said, it will be easy to con-
ceive how, in defining a term, standing for any very
complex idea, other terms may be introduced, that
also denote compound ideas, though of an inferior
class. For the first idea being resolvable into others
less complicated ; the definition, which enumerates
these component ideas, must consist of the names by
which they are expressed. And if it so happen, that
the ideas of this second class are also unknown, their
terms, too, ought to be still farther defined. In this
manner may a series of definitions be carried on, un-
til we arrive at the names of simple ideas, which not
being defixuable, the analysis must necessarily cease.
And thus we see, that as our simple ideas are the
materials and foundation of knowledge, so the names
of simple ideas may be considered as the elementary
pails of language, beyond which we cannot trace the
meaning and signification of words. When we come
to them, we suppose the ideas they stand for already
kno^vn ; or, if they are not, experience alone must
be consulted, and not definitions or explications. And
here it is v/ell v/orth our notice, that a« the names of
these our original conceptions, constitute the primi-
tive and fundamental articles of speech, upon which
the whole superstructure of human language is built,
10 DUNCAN'S ELEMENTS
so they are, of all others, the least doubtful and un-
certain in their si gnili cation. Because, standing each
for one simple perception, not precariously excited
in the mind, but the effecL of certain posv'ers in things,
fitted to produce that sensation in us ; there is no
danger of error or mistake. He that once knows
siveetness to be the name of the taste received from
sup"ar, whiteness of the colour in snow or tniik, and
heat of the sensation produced by approaching the
fire, will not be apt to misapply those words, or -^n-
nex them to perceptions of a different kind. And as
the names of complex ideas may all be resolved into
these primitive terms, it is apparent, tl.at we are suf-
ficiently provided with the means of communicating
-our thoughts one to another ; and that the mistakes
so frequently complained of en this head, are wholly
owing to ourselves, is not sufficiently defining th.e
terms we use, or perhaps not connecting them with
clear and determinate ideas.
CHAP. VI.
OF DEFINITIOX, AND ITS SEVERAL KINDS.
Sec. l.—'TIie variety of Dejinitions firoceeds from the
-various Ajijilication of Words.
H
AviNG laid these foundations, shovm v.hat words
are, and what are not definable, and taught the man-
ner of resolving our notions, as v/eli as language it-
self, into its first and original principles ; v.^e now pro-
ceed to explain a little more particularly the nature
of a definition, and the several kinds made use of, ac-
cording to the different viev/s m.en have in communi-
cating their thoughts one to another. Definitions are
inteiided to make known the meaning of words stand-
OF LOGIC. 81
ing; for complex ideas ; aiid were we always careful
to form those ideas exactly in our minds, and copy
our definitions from that appearance, much of the
confusion and obscurity coniplaiued of in languages
might be prevented. But, unhappily for us, we are
by no means steady in the application of names, re-
ferring them sometimes to one thing, sometimes to
another ; which often creates great uncertainty in
their signification, and obliges us to give a different
turn to our definitions, according to the different re-
ference of the terms defined. In order, therefore, to
render this -whole matter as clear and obvious as pos-
sible, we shall first consider to what it is that names,
in the use of language, are most commonly applied ;
and then from the variety of this application, endea-
vour to account for the several methods of denning,
mentioned in the writings of logicians.
Sec. II.— JVords harve a threefold Reference ; to our Oxm
Ideas^ those rf others^ and the real being of tilings.
Words then have manifestly a threefold reference.
First, and more immediately, they denote the ideas
in the mind of him who uses them ; and this is their
trae and proper signification. When a man speaks,
it is that he may be understood ; and the words he
employs to convey his thoughts, are such as by use he
has learned to connect with the ideas then present to
his mind. But because those with whom we converse,
are also supposed to know the meaning of the terms
we use, hence, secondly, we consider our words as
signs, likewise, of the ideas in their minds ; and this
is the foundation of what is called propriety in lan-
guage, when men take care to affix such notions to
their words, as are commonly applied to them by those
of most understanding in the country where they live.
The third and last reference of words is to things
S2 DUNCAN'S ELEMENTS
themselves. For many of our ideas are taken from
the several objects of nature, where v/ith we are sur-
rounded ; and being considered as copies of things
really existing, the words, by which they are express-
ed, are often transferred from the ideas themselves,
to signify those objects which they are supposed to
represent. Thus the word, sun, not only denotes the
idea excited in the mind by that sound, but is also fre-
quently made to stand for the luminous body itself,
which inhabits the centre of this our planetary system.
Now, according to this threefold application of names,
their definitions, and the manner of explaining them,
must be various ; for it is one thing to unfold the ideas
in a man's own mind, another to describe them, as
they are supposed to make their appearance in the
minds of others ; and lastly, it is something still dif-
ferent, to draw images or pictures, that shall carry in
them a confonTiity to the being and reality of things.
But we shall treat of each in order.
Sec. III. Definitions of the Name teach only the Con-
nexion of our Words and Ideas, and are therefore ar-
bitrary.
First, then, when we consider words, as signs of the
ideas in the mind of him who uses them ; a definition
is nothing else, but such an explication of the mean-
ing of any term, as that the complex idea annexed to
it by the speaker, may be excited in the understand-
ing of him with whom he converses. And this is
plainly no more than teaching the connexion of our
words and ideas,. that others may understand the sense
of our expressions, and know distinctly what notions
we affix to the terms we use. When we say, for in-
stance, that by the word square we mean a figure
bounded by four equal sides, joined together at right
angles j what is this but a declaration, that the idea
OF LOGia 83^
of a quadrilateral, equilateral, rectangular figure, is
that which in discourse or writing we connect with
the term square ? This is that kind of definition, which
logicians call the dejinitlon of the name ; because it dis-
covers the meaning of the words or names we make
use of, by showing the ideas for which they stand.
Now, as sounds are of themselves indifferent to sig-
nify any ideas, hence it is plain, that the definitions
of names are arbitrary, every man having a liberty to
affix what notions he pleases to his words. But the
convenience of communication making it necessary
for men speaking the same language to agree as near-
ly as possible in the signification of sounds, a con-
formity has accordingly been studied. Nevertheless,
we find that differences will, from time to time, creep
in, which must create great confusion in men's dis-
courses and reasonings, if they are not careful to de-
fine their terms, that their signification may be kept
fixed and steady, and lie always open to the view of
the mind. The writings of the mathematicians are
a clear proof, how much the advancem.ent of human
knowledge depends upon a right use of definitions,.
For as by means of them they every where preserve
the same detennined significations to their words,
hence there is little dispute as to the meaning of their
expressions, almost all men understanding them in the
same sense- And thus it happens, that such as apply
their thoughts this way, having perfectly the same
views of things, readily comprehend the discoveries
already made, and are thereby enabled with joint la-
bour, and an exact conforijpity of notions, to carry on
the improvement of this branch of knowledge. And
if men in other parts of learning, were alike careful
to fix the meaning of their terms, the progress of
science must be greatly furthered, and all those ver-
bal disputes, that now so much interrupt the course
©f our improvements, might be prevented.
34 DUNCAN'S ELEMENTS
Sec. IV. — Dejirdtions of the JSfamenot always true and
real Definitions ;
This then ought to be our first care, when we en-
ter upon a design of illustrating any particular branch
of study ; to ascertain our ideas, and mark the names
by which they are expressed. And although defini-
tions of words are indeed arbitrary, (for a man may
affix what ideas he pleases to his terms, nor can any
one contest this liberty with him,) yet it will be prop-
er to conform, as near as possible, to common accep-
tation, that thereby our thoughts may find a more ea-
sy and ready entrance into the minds of others. If
it should now be asked, Avhat are the rules of a good
tlefiniticn ; I answer, that as in definitions of the name,
we aim at no more than teaching the connexion of
vv ords and ideas ; every contrivance, by which we are
enabled to excite the idea annexed to any Avord in the
mind of another, will serve the purpose of a defini-
tion. Now the ideas v/e join with our words are of
^wo kinds : either such as we have reason to believe
ure already in the minds of others, though perhaps
they knov/ not the names by whicii they are called ;
or such as, being new and of our own formation, can
be no otherwise made knoAvn than by a description.
In the first case, there is no necessity for laying open
the idea itself, because being already known, any con-
trivance to remind us of it is sufllcient. When we
say, for instance, that a clock is an instrument^ by ivhich
we measure the hours of the day ; it is plain, that the
idea answering to the word clocks is not here unfold-
ed ; but we being before nand supposed to have an
idea of this instrument, are only taught by what name
it is called. Now in this sense, the names of even
simple ideas may be denned. For, by saying that
•ivhite is the colour we observe in snow or milk, heat
the sensation produced by approaching the fire, v/e
OF LOGIC. 85
srufficientiy make known what ideas Vv'e connect with
the terms, ivhite and heat^ which is the true purpose
of a definition of the name. Hence it appears, that
many of those explanations of words, which logicians
call definitions of the name, are not definitions in a
true and proper sense, that is, such descriptions of
ideas, as would serve to excite them in the mind of
another, even supposing him before wholly unac-
quainted with them, but merely contrivances to re-
mind us of known ideas, and teach us the names by
which they are called.
Sec. V. — But only ivhen thexj Coincide with the Defini'
tion of the Thin^.
But where the ideas we join with our words, are
new and of our own formation, there they are to be
laid open by a description, because, being supposed
unknown to others, we must first raise them in their
minds, bef:)re they can learn to connect them with
any particular names. And here it is, that the defi-
nition of the name coincides with what logicians call
the definition of the thing, as in either case we pro-
ceed by unfolding the idea itself for which the term
denned stai"ids. And indeed this alone is what con-
stitutes a definition, in the true and proper sense of
the word, as will appear more fully afterwards, when
v/e come to consider the terms v/e use, as referred to
the real objects of nature. We'sh'all therefore post-
pone this consideration of the definition of the name,
till we come to treat of the definition of the thing,
w^hen it will m^ore naturally fall in our way. It may
not, however, be amiss to observe, that when we say
the definitions of the name are arbitrary, we mean
not that the descriptions of ideas are so too. For
every idea having a peculiar appearance of its own,
by which it is distinguished from all others, nothing
86 DUNCAN'S ELEMENTS'
is more evident, than that the description must be
such as to exhibit that precise conception. But then
the connexion of any- idea, with the name ay which it
is expressed, being, as we have said, wholly arbitrary,
the considering the description of that idea as the
definition of that particular nam.e must be so too. Sa
that although definitions, considered as descriptions
of our ideas, are steady and invariable, yet the appli-
cation of them to particular sounds, (which is all that
we understand by the definition of the name) is whol-
ly a work of our own free choice.
Sec. VI. — Definition of Words according to the com-
mon use of Language not Arbitrary.
But secondly, besides considering words as the
signs of our own ideas, we are also very apt, on many
Gccasi-ons, to refer them to the ideas in the minds of
other men. Now, to define a term, in this view, is to
investigate its meaning or acceptation, according to
the common use of speech. Here then it is plain,
that definitions are not arbitrary. For although in-
regarding words as the marks of our own ideas, we
may give them what meaning we please ; yet when
we consider them in reference to the thoughts of
others, they have a fixed and steady signification;
namely, that which custom and the propriety of Ian-
guage has assigned them. The words, ability and
genius^ nnay, by any man, be made to stand for one
and the same idea in his own mind, and if he takes
care to advertise us of this, he is at liberty to use them
promiscuously. But if the common course of lan-
guage hath confined the word genius to express the
natural strength and talents of the mind, and the
word ability to denote those which are acquired, v/ho-
ever pretends to explain the proper acceptation of
tiiese terms, is bound to take notice of tiiis difference.
OP LOGIC. 57
As propriety of speech makes our language intelligi-
ble, and gives our thoughts a ready entrance into the
minds of others, it well deserves our application and
care. The best vray to acquire it is from the writings
and discourses of those who seem to ha'\ e had the
clearest notions, and to have applied their terms with
the exactest choice and fitness.
Sec. VII. — D'ifimtio7is of the Thing refer to the real
Objects of Xattire.
We come now to the third and last species of defi-
nition, that namely, which considers words as refei'-
red to things themselves. And here it is plain, we
are not at liberty to feign and fashion our explications
at pleasure, but being tied down to the real objects of
nature must study a conformity to things themselves.
When we define, for instance, the sun, considered as
that being who possesses the centre of our system,
and diffuses heat and light to the planets around him ;
it is not enough that we give an account of the idea,
answering to that word in our minds. We must
ftirther take care, that the idea itself carries in it a
real conformity to the object it is supposed to repre-
sent. And hence it is, that all definitions of this kind,
when justly made, are in reality pictures or repre-
sentations, taken from the being and existence of
things. For they are intended to express their na-
ture and properties so as to distinguish them from
all others, and exhibit them clearly to the vievv of the
mind. 'Tis for this reason that logicians call them
definitions of things, because they are supposed to
refer, not so much to the ideas in the understanding,
as to the things themselves represented by those
ideas.
S8 DUNCAN'S ELEMENTS
Sec. VIII.— Grow wc? of the distinction between the aV-
fcnition of the Name and of the Thing.
And this also lets us into the ground of that dis-
linctlon so universally received betv/een definitions
of the name and of the thing. The first are arhitra-
rv, and not liable to debate or contradiction. The
second are propositions, capable of proof and illus-
tration, and which may therefore be contested. The
reason is obvious. Definitions of the name serve on-
ly to mark what ideas we connect with our words. —
And as sounds are of themselves indifferent to signify
any ideas, vre are entirely at liberty to affix to them
what notions we please. But it is otherwise in the
definition of the thing. For here our words serving
to denote particular beings in nature, cannot be the
signs of any ideas at jjleasure, but of such only as
carry in them a conformity to the several objects to
which the vrords refer. A man may use the term,^
square^ to express that idea, which others denote by
the v/ord, triangle, and define it accordingly. In this
case, indeed, he recedes from the common forms of
speech, but his definition cannot be charged with
falsehood. He tells us that by a square he means a
three-sided figure ; and wJio can dispute the truth of
this, if he really all along uses the word in that sense ?
I would only observe, that by changing thus the
meaning of words, we change not things themselves,
or their relations and habitudes one towards another.
These are at all times the same and invariable, nor
have any dependence upon the fancy and caprice of
men. It is true,- the properties of the tnangle may,
after this definition, be affirmed oi th^ square ; but as
in either case, the idea to v/hich these properties be-
long, is the same, the propositions only expressing
our judgments, and not our judgments themselves,
suffer a seeming variation.
OF LOGIC. 89
Sec. IX. — A fireviou-s connexion betiueen A^ames and
Things^ cuts off all Arbitrary Explications.
But where words are made to denote particular ob-
jects, previous to any definitions given, there arbitra-
ry explications cannot have place. For in this case,
we are not put upon explaining what ideas we con-
nect v/ith our Avords, biit a connexion being already
supposed between the name and the thing signified,
our business is to unfold that idea by which the ob-
ject itself is most clearly and distinctly represented.
Thus the word gold^ denotes that metal which is of
highest value among men, and goes farthest in the
way of commerce. This connexion being once set-
tled, we are no longer left to arbitary definitions, but
must describe it by such properties as are really to be
found in it, and vriil best serve to distinguish it when
it comes in our way ; as by saying it is a substance
yellow, very hea\y, malleable, fusible, 8cc.
Sec. X. — Whij Mathematical Definitions have been ac-
counted mere Definitions of the JVaine ;
From what has been said, it appears, that in the
language of logicians, definitions of the thing respect
only substances and beings that have a real existence
in nature, serving to describe them by their proper-
ties and attributes. And this, I doubt not, is the rea-
son, that the definitions of the mathematicians are
not considered as definitions of the thing, but of the
name ; because the ideas therein described, are the
mere creatures of the understariding, and not suppos-
ed to be copied from patterns existing w-ithout us.
A circle, a triangle, a square, &cc. such as mathema-
ticians conceive them, are no where to be found in na-
ture, that we know of. Hence it might justly be ac-
counted absurd, to call our definitions of these, defini-
tions of the things when thev serve not to describe anv
M
90 ■BUNCAN^s "ELEMENTS
real objects of nature, but merely to unfold the con-
ceptioris of the mind. And yet if we look into tiie
iTiritter narroAvly, we shall find, that the rules follow-
ed in these deRnlticns are precisely the same with
those which logicians have laid down for the definition
of the thing. All the several species of figures are
described by their prcpertics, some of which are com-
mon to different ranks, others peculiar to the tribe
defined. The common properties constitute what
iog-icians call the genus, and those tliat are peculiar,
the difcraice Now the genus and dijference make
lip the logical dciinition of the thing, as will be more
clearly understood from what follows.
Sec. XI. — When yet they coincide rjith the logical dcf-
ration of the things and therefore ought not to be ac-
counted arbitrary.
I am therefore, apt to think, that mathematical
definitions, as they are of the same general with the
definitions of substances, and subject to the same
rules, have been improperly considered as mere defi-
nitions of the name, in which we are left wholly to
arliitrary explications. For however wx may change
the name of one figure for another in discourse or
writing, using the term square to denote a triangle^
or tlie word triangle to express a square, it is certain
the ideas themselves are invariable, and no less capa-
ble of being distinguished by their properties, than
the several species of substances. Thus if we
suppo3e the v/ord square to denote that species of fig-
ures, Avhose sides severally subtend quadrants of a
circumscribed circle, we shall find oui'selves equally
siiut out from arl'jitrary explications, as in the defini-
tion of the names of substances. For as this happens
in no figures but those which are bounded by four
equal sides joined together at right angles ; itfollov/s
OF logic: 91
evidently, that the true and proper deiinitlon of a
square, is that which exhibits the precise idea here
mentioned, and no other, to the mind. And thus it
appears, that the common division of definitions, into
those of the name and thing, is not sufficiently calcu-
lated to give us right apprehension.s, as to v.hat is and
what is not arbitrary in the explication of ^vords. It
may not, therefore, be improper, if we here endeavor
to clear up this matter a little, and free it from those
obscurities in wiiich it has hitherto been involved.
To this end we shall premise the follov.'ing observa-
tions.
Sec. XII. — Drjirdiions^ properly speakings never re-
gard Things.^ but merely our Qi:;n Ideas.
1 . First, that whatever logicians may pretend about
the definition of the thing, it is yet certain, that none
of our definitions, when pursued to their source, re-
gard immediately things themselves, but merely the
ideas in our ovrn mJnds. This, I doubt not, will ap-
pear a paradox to many, wlio will be apt to enquire,
v/hether the definition oi gold, be not taken from that,
metal, independent of the various conceptions of men
about it. To this I answer, that indeed in framing
cur idea of g-cld, v/e regard chieHy the thing itseli,
uniting in our conception sucli properties as are most
conspicuous, and csrve best to distinguish it from
other metals, to which it may bear any resemblance.
But as it is by this idea alone that gold is known to
us, so in describing it to others, we aim at nothing
more than to transfer the same conception into their
minds. Nov/ this can no otherv/ise be done, but by
enumerating the several properties of which our own
complex notion is formed. And indeed it were in
the highest degree' absurd to imagine, that men in,
explaining things: to others, should make use of any
$2 DUNCAN'S ELEMENTS
marks or characters, but those by which they are
known to themselves. Hence it comes to pass, that
ail our defmitions are in fact nothing else but trans-
cripts of the ideas in our minds. Where these are
imperfect, the definitions must be so too ; where
they are just and adequate, the copies taken from
them, if drawn out with accuracy and care, cannot
fail to exhibit tlie object described. And this v/ill
very well serve to account for that great diversity of
definitions we often m^eet with, even of one and the
same object. Because men, in consequence of their-
difFerent pursuits and applications, falling often into-
difierent views of things, must needs vary no less in
their definitions, than in the ideas themselves from
Avhich these definitions are copied. He, whose ob-
servation goes no farther than the more obvious quali-
ties of gold, will content himself with describing it b)~
its colour, weight, and perhaps malleability and fusi-
bility. On the other hand, a goldsmith, having en-
quired farther into the nature of that metal, and find-
ing several other properties that equally belong to it,
will be apt to take these also into his complex idea,
and accordingly introduce them in a definition. Hence
his description will add to the former, fixedness, and
solubility in egua regia^ Sec. And so in proportion as
men's various pursuits lead them into a more accurate
examination of things, their explications will take a
diiTerent tura, suitable to the ideas they have fi^amed
rrithin themselves. , . ■
Sec. yA\\.—-Ijhtivrticn betnveen the Dcfir.ition cf the
name and thing useless^ and to be rejected.
2. This then being evident, that our definitions re-
spect not things themselves, but the ideas in our own
minds ; I would in the next place observe., that the
distinction cf them into these of the name and thing,.
OF LOGIC. 93
is altogether useless, and tends rather to mislead us.
than give right apprehensions of the subject in hand.
For thus men are apt to fancy, that many of their de-
finitions are expressive of the real essence of things,,
whereas they are in ti'uth no more than transcripts of
their own ideas. And as it sometimes falls out, that
these ideas are not collected with sufficient care, from
the objects they represent ; we find, by experience,
that a mistaken idea never fails to occasion a mistake
also in the definition. But this could not happen, were,
our definitions copied from things themselves : be-
cause their essences being immutable and always the
same, the definition would in this case serve to cor-
rect the idea, and might be considered as a standard,
by which to judge whetiier tlie idea Avas rightly fram-
ed. I deny not, that vvords are often transferred from
our ideas to signify the objects which these ideas,
represent ; as when we talk of the sun, the earth,
men, and other animals. But then let it be observed,
that as these objects are only known to us, by the ideas-
of them in our minds ; so, in describing them to oth--
crs, all we aim at is, distinctly to lay open our concep-
tions about them. Hence it appears, that what lo-
gicians call a definition of the thing, is in truth no more
than an unfolding of the idea, by "\vhich that thing is
represented to the understanding. But now in math-
ematicq.1 definitions, and indeed all others whatsoever,
this also is our whole aim and intent, to exhibit and
lay open thos.§ ideas,, of which tlie words we use are
the signs^ And thus it happens, that in innumerable,
instances, v/hat logicians call the defnitio?t of the namey.
is yet found to coincide witii and proceed by the very
same rules, d^^Xh^ defnition of the thing ; which clear-
ly demonstrates the necessity of banisliing this frivo-
lous distinction, and establishing some precise and
determinate notion, expressive of tlie ti'ue nature of a
definition, and comprehending it in its full extent.
94 DUNCAN'S ELEMENTS
Sec. XIV. — Drfmitions in all cases descrijuions of cur
Ideas.
Nor will this appear so diujcult a task, if we call to
Tnind, that v/ords are in all cases the signs of" our
ideas, and no otherwise signify things, than as they
stand for those ideas by v/hich things are represented
to the understanding. By defining our words, there-
fore, vv'e can mean no more, than the laying open to
the view of otliers, the ideas of v\'hich these v/orcls are
the signs. For thus it is, that the meaning of our
expressions comes to be known, and that we find our-
fcclves capable of transferring our thoughts and con-
eeptions into the minds of those with whom we con-
verse. Where wcrds are referred to things them-
selves, there we explain tlje ideas by vrhich thess
things are represented ; v.iiere they denote concep-
tions framed by the mind, tliere Ave la.y open these
conceptions, and endeavour to exhibit them accord-
ing to their real appearance Avithin our own breasts.
But in both cases, it is our ovrn ideas, it is the per-
cepiions of our ov.n minds, either as taken frcm things
without, or framed by the understanding itself, that
we explicate and unfold.
Sec. XV. — J\''ot ari-lirary^ a-i being confined to the Kc-
jiresentalion of certain cleterrniiiate J\^otiohs.
And thus Ave have at leneth settled the true and
genuine notion of a definition, comprehending all its
varieties, from AAiiateA'cr science taken^- or to Avhatev-
er object extended. For from Avhat aa'c have said, it
evidently follows, that a definition is the unfolding of
some conception of the mind, answering to the wx>rd
or term made use of as the sign of it. Now, as in
exhibiting any idea to another, it is necessary that
the description be such as may excite that precise
idea in his mind :. hence it is nlain, that deflmticns>
OF LOGIC. 95
properly speaking, are not arbitrary, but confined to
the representing- of certain determinate settled no-
tions, such, naniely, as are annexed by the speaker
or \^-riter to the words he uses. As, nevertheless, it
is universally allowed that the signilication of words
is perfectly voluntary, and not the effect of any natur-
al and necessary connexion befween them and the
ideas for vfhicli they stand, some mav perhaDs won-
der why definitions are not so tC'f>. In order, there-
fore, to unravel this difficulty, and show distinctly
Avhat is, and what is not arbitrary in speech, we must
carefully distinguish between the connexion of our
words and ideas, and the unfolding of the ideas them*
selves.
Sec. XVI. — T/ie Ccrmexion bet^.veen Words avd Ideas,
a Jic-fcciiy voluntary Establhlnnenl.
First, as to the connexion of our words and ideas,
this, it is plain, is a purely arbitrary institution. When,
for instance, vre have in our minds, the idea of any
particular species of metals, the calling it by tlie nam^e
gokU is an effect of the voluntary choice of men speak-
ing the same language, and not of any peculiar apt-
ness in that sound to express that idea. Other na-
tions, we find make use of diiTerent sounds, and with
the same effect. Thus aurum denotes that idea in
Latin, and or in French. And even the word gold
itself, would have as well served to express the idea
of that metal vvhich we call silver^ had custom in the
beginning so established it.
bee. XVII, — The JDescri/iizona of Ideas not so, but
bouudsd to the Refivesentaiion of that precise A}.-
pearcnce by nvhick they arc dhtinguished among
themselves.
But although we are thus entirely at liberty, iu
connecting any idea with any souna, yet it is quite
^6 DUNCAN'S ELEMENTS
otherwise in unfolding the ideas themselves. For
every idea, having a precise appearance of lis ov/n,
by which it is distinguished from every other idea ;
it is manifest, that in laying it open to others, we must
study such a description, as shall exhibit that pecu-
liar appearance. When we have formed to our-
selves the idea of a figure bounded by four equal
sides, joined together at right angles, we are at lib-
erty to express that idea by any sound, and may call
it either a square or a triavgle. But whichever of
these names we use, so long as the idea is the same,
the description, by which we would signify it to an-
other, must be so too. Let it be called square or tri-
angle^ it is still a figure having four equal sides, and
all its angles right ones. Hence we clearly see, what
13, and what is not arbitrary in the use of words. The
establishing any sound, as the mark of some deter-
minate idea in the mind, is the effect of free choice^
and a voluntary combination among men. And as
diflcrent nations make use of different sounds, to de-
note the same ideas, hence proceeds all that variety
of languages which we meet with in the world. But
when a connexion between our ideas and words is
once settled, the unfolding of the idea answering to
any word, which properly constitutes a definition, is
by no means an arbitrary thing. For here, as I have
already observed, we are bound to exhibit that pre-
cise conception, which either the use of language or
our own particular choice, hath annexed to the term
we use.
Sec. XVIII. — Causes of the Obscuriiy that has hither-
to fierfilexed the Theory of Definitions.
And thus it appears, that definitions, considered as
descriptions of ideas in the mind, are steady and inva-
riable, being bounded to the representation c: these
OF LOGIC.
9r
precise ideas. But then in the application of defini-
tions to particular names, Vv e are altogether left to
our own free choice. Because as the ({onnectinp- of
any idea with any sound, is a perfectly arbitrary insti-
tution ; the applying the description of that idea, to
that sound, must be so t<5o. When, therefore, IcP-i-
cians tell us, that the definition of the name is aibi-
trary, they mean no more than this ; that as dinerei>^
ideas may be connected with any term, accord;np--to
ti:e good pleasure of him that uses it, in like manner
may different descriptions be applied to that term.,
suitable to the ideas so connected. But this connex-
ion being settled, and the term considered asthes'^n
oi some fixed idea in the understandings, we are So
longer left to arbitrary explications, butm.ust study-
such a description as corresponds with that prec'iVe
idea. Now this alone, according to what has b^-a
before laid do^vn, ought to be accounted a definition
V.'iiat, I am apt to think, has occasioned no small
confusion m this matter is, that many explanations
01 words, wiiere no idea is unfolded, but merely the
connexion between sopie word and ide^ asse-ted
have yet been dignified with the name of definitions'
1 bus, m the instance before given, when we say that
a cock IS an instrument by wiiich Vv-e measure ^ime •
tiiis is by some called a definition. And yet' it is
plain, that we are beforehand supposed to have an
idea of this instrument, and only taught that the wo-d
dock, serves in common language to denote that idea
Ly tms rule all explications of words in our d-ctiora-
ries will be definitions ; nay, as was already observ-
ed, the names of even simple ideas may be thus de-
hned. li/me, we may say is the colour we observe
m snow or milk, heai the sensation produced by an-
proachmg the fire, and so in innumerable other in-
stances. But these, and all others of the like kind,
98 DUNCAN'S ELEMENTS
are by no means definitions, exciting new ideas in
tiie understanding, but merely contrivances to remind
us of known ideas, and teach their connexion witli
the established names. It is, nevertheless, worth
our notice, that what logicians call definitions of the
name, extend properly no farther than these explan-
ations, serving to mark the comiexion of our ideas and
words ; and are therefore justly accounted arbitrary,
inasmuch as the connexions themselves are altogeth-
er so.
Sec, XIX. — Comfilex ideas alone capable of that kind of
description ivhich goes by the name of a definition.
But now in. definitions properly so called, we first
consider the term we use, as the sign of some inward
conception, either amiexed to it by custom, or our own
free choice ; and then the business of the definition is
to unfold and explicate that idea. As therefore the
wliole ai:t lies, in giving just and true copies of our
ideas ; a definition is then said to be perfect, when it
serves distinctly to excite the idea described in the
mind of another, even supposing him before wholly
unacquainted with it. This point settled, let us next
enquire into v/hat those ideas are which are capable of
being thus unfolded. And in the first place, it is evi-
dent, that all our simple ideas are necessarily exclud-
ed. Vv'e have seen already, that experience alone is
to be consulted here, insomuch, that if either the ob-
jects, whence they are derived, come not in our way,
or the avenues appointed by nature for their reception
are wanting, no description is sufficient to convey them
into the rnind. But where the understanding is al-
ready supplied with these original and primitive con-
ceDtions,*a3 they may be united together in an infinity
.of different forms ; so may all their several combina-
tions be diiitinctly laid open by enumerating the sim-
OF LOGIC. 99
pie ideas concerned in the various collections, and
tracing the order and manner in which they are linked
one to another. Now these combinations of simple
notices constitute what we call our complex notions ;
whence it is evident that complex ideas, and those a-
lone, admit of that kind of description, which goes by
the name of a definition.
Sec. XX.-^rF/ze7z a comfilex idea ?nay be said to be fully
v.nfolded.
The business of definitions is now, I think, pretty
plain. They are, as we have seen, pictures or repre-
sentations of our ideas ; and as these representations
are then only possible, when the ideas themselves are
complex ; it is obvious to remark, that definitions can-
not have place, but Avhere we make use of terms,
standing for such complex ideas. But perhaps the
reader may still expect, that we should enter a little
more particularly into the nature of a definition, de-
scribe its parts, and show by what rules it ought to
proceed, in order to the attainment of its proper end.
To give, therefore, what satisfaction we are able upon
this point, wx must again call to mind, that the design
of a definition is, so to unfold the idea answering to
any term, as that it may be clearly and distinctly
transferred into the mind of another. Eut now our
complex ideas, which alone are capable of this kind
of description, being, as we have said, nothing more
than different combinations of simple ideas ; we then
know and comprehend them perfectly, when we knov/
the several simple ideas of which they consist, and
can so put them together in our minds, as is necessa-
ry towards the framing of that peculiar connexion,
which gives every idea its distinct and proper appear-
ance.
100 DUNCAN^s ELEMENTS
Sec. XXL— Z'wo things required in a definition: to en-
umerate the ideas^ and explain the manner of their
CGTdbination.
Trro things are therefore required in every defini-
tion. First, that all the original ideas, out of v/hich
the complex one is formed, be distinctly enumerated.
Secondly, that the order and mannei; of combining
them into one conception, 'be clearly explained. —
^'V'.here a de/inition has these requisites, nothing is
•wanting to its perfection ; because every one wiio
reads it, and understands the terms, seeing at once
v/hat ideas he is to join together, aid 'also in what
manner, can at pleasure form in his own mind the
conplex conception answering to the term denned.
Let us, for instance, suppose the word, .s5-^;are, to stand
for that idea, by which Ave represent to ourselves a
figure, whose sides subtend quadrants of a circum-
sci-ibed circle. The parts of this idea, ?.re the sides
]:)oundh;g the figure. These must be four in num-
ber, and all equal among themselves, because they
ere each to subtend a fourth part of the same circle.
But besides these component parts, we must also take
: notice of the manner of putting them together, if v/e
should exhibit the precise idea, for which the v/ord
square here stands. For four equal nght lines, any
■ how joined, will not subtend quadrants of a circum-
scribed circle. A figure with this property, must
have its sides sta.nding also at right angles. Taking
in, therefore, this last consideration, respecting the
-manner of combining the parts, the idea is fully de-
scribed, and the definition thereby rendered complete.
P'or a figure, i)ounded by four equ?J sides, joined to-
gether at right angles, has the property required*;
aiid is, moreover, the only riglit-liaed figure to which
that property belongs.
OF LOGIC. . 101
Sec. XXII. — Hovj -ve are to proceed^ to arrrve at just
and adequate definitions.
And nuw, I imagine, it will be obvious to every one
in v/h"at manner vre ought to proceed, in order to ar-
rive at just and adequate definitions. First, we are to
take an exact \'iew of the idea to be described, trace
it to its original principles, and mark the several sim-
ple perceptions that enter into the composition of it.
Secondly, we are to consider the particular manner
in which these elementary ideas are combined, in or-
der to the forming of tliat precise conception, for
which the term Ave make use of stands. When tiiis
is done, and the idea v\-]iolIy unravelled, we ha^-e noth-
ing more to do, than fairly transcribe the appearance
it makes to oirr ovm minds. Such a description, by
distinctly exhibiting the order and number of our
primitive conceptions, cannot fail to excite, at the
same time, in the mind of every one that reads it, the
complex idea resulting from them ; and therefore at-
tains the true i:AiCi proper end of a definition.
OF THE CO'TPOSITIOX AXD RESOLUTION OF OUR
IDEAS, AND THE RULES OF DEFINITION
THENCE ARISING.
Sec. I In cov7Jiou7uli"g cur Idras^ tve proceed by suC'
cessive gradatioji.
JL HE rule laid down in the foregoing chapter is gen-
eral, extending to all possible cases ; and is, indeed,
that to which alone vve can have recourse, where any
doubt or diaiculty arises- It is not, however, neces-
sary, that we should practice it in every particular
instance. Ivlany of our ides.s are extremely ccmpli-
102 DUNCAN'S ELEMENTS
cated ; insomuch that to enumerate all the simpM
perceptions out of which they are formed, would be
a very troublesome and tedious work. For this reas-
on, logicians have established certain compendious
rules of denning, of which it may not be amiss
here to give some account. But in order to the bet-
ter understanding of what follows, it will be necessa-
ry to observe, that there is a certain gradation in the
composition of our ideas. The mind of man is very
limited in its views, and cannot take in a great num-
ber of objects at once. We are, therefore, fain to
proceed by steps, and make our first advances sub-
servient to those which follow. Thus in forming our
complex notions, we begin at first with but a few sim-
ple ideas, such as we can manage with ease, and
unite them together into one conception. When we
are provided witli a sufiicient stock of these, and have,
by habit and use, rendered them familiar to our minds,
they become the component parts of other ideas, still
more complicated, and form what v/e may call a sec-
ond order of compound notions. This process, as is
evident, may be continued to any degree of composi-
tion we please, mounting from one stage to another,
and enlarging the number of combinations.
Sec. II, — Hence ideas of this class best comprehencledy
when ive advance gradually through all the several
orders.
But now in a series of this kind, whoever would
acquaint himself perfectly with the last and highest
order of ideas, finds it much the most expeditious
method, to proceed gradually through all the inter-
mediate steps. For was he to take any very com-
pounded idea to pieces, and without regard to the
several classes of simple perceptions, that have al-
ready been formed into distinct combinations, break
OF LOGIC. 105
ill at once into its original principles, the number
would be so great, as perfectly to confound the imag-
ination, and overcome the utmost reach and capacity
of the mind. When we see a prodigious multitude
of men, jumbled together in crowds, without order,
or any regular position, we find it impossible to ar-
rive at an exact knowledge of their number. But if
they are formed into separate battalions, and so sta-
tioned as to. fall within the leisurely survey of the
eye ; by viewing them successively, and in order, we
come to an easy and certain determination. It is the
same in our complex ideas. When the original per-
ceptions, out of which they are framed, are very nu-
merous, it is not enough that vv"e take a view of them
in loose and scattered bodies. ^Ve must form them
into distinct classes, and unite these classes in a just
and orderly manner, before we can arrive at a true
knowledge of the compound notices resulting from
them..
Sec. III. — Our Definitions ought to keep, pace with our
Ideas^ and observe a like gradation.
This gradual progress of the mind to its compound
notions, through a variety of intermediate steps, plain-
ly points out the manner of conducting the definitions
by which these notions are conveyed into the minds
of others. For as the series begins with simple and
easy combinations, and advances through a succes-
sion of different orders, rising one above another in
the degree of composition ; it is evident, that in a
train of definitions expressing these ideas, a like gra-
dation is to be observed. Thus the complex ideas of
the lov/est order, can no otherwise be described, than
by enumerating the simple ideas out of which they
are made, and explaining the manner of their union.
But then in the second, cr any succeeding order, as
104 DUNCAN'S ELEMENTS
they are formed out of those gradual combinations^
that constitute the inferior classes, it is not necessa-
ry in describing them, to mention one by one, all the
simple ideas of which they consist. They may be
more distinctly and briefly unfolded, by enumerating
the compound ideas of a lower order from whose
union they result, and which are all supposed to be
a'lrep.dy knovrn, in consequence of previous definitions.
Here then it is, that the logical method of defining-
takes place ; which, that we may the better under-
stand, I shall explain somewhat more paitxularlv,
the several steps and gradations of the mind, in com-
pounding its ideas, and thence deduce that peculiar
ibrm of a deiinition, which logicians have thought nt
to establish.
Sec. IV. — The stcfis by ivhich the Miizd proceeds from
Particular to General Ideas.
All the ideas we receive, from the several objects
of nature that surround us, represent distinct individ-
uals. These individuals, wdien compared together,
are found in certain particulars to resemble. Hence,
by collecting the resembling particulars into one con-
ception, we form the notion of a s/iecics. And here
let it be observed, that this last idea is less compli-
cated than that by wdiich we represerit any of the
particular objects contained under it. For the idea
of the species excludes the peculiarities of the sever*
ai individuals, and retains only such properties as are
common to them all. Again, by comparing several
species together, and observing their resemblance,
we form the idea of thd gcm:s ; where, in the same
manner as before, the composition is lessened, because
vv^e leave out v/hat is peculiar to the several species
compared, and retain only the particulars wherein
they agree. It is easy to conceive the mind, proceed-
OF LOGIC. los-
ing thus from one step to another, and advancing
through its several classes of general notions, until at
last it comes to the highest genus of all, denoted by
the word beings where the bare idea of existence is
only concerned.
Sec. V. — The conduct of the Mind in comjiounding its
Ideas, as it advances through the different orders of
perception.
In this procedure, we see the mind unravelling a
complex idea, and tracing it in the ascending scale,
from greater to less degrees of composition, until it
terminates in one simple perception. If now we take
the series the contrary way, and beginning v>-ith the
last or highest genus, carry our vievv' downwards,
through all the infe^or genera and species, quite to
the individurls ; we shall thereby arrive at a distinct
apprehension of the conduct of the understanding in
compounding its ideas. For in the several classes of
our perceptions, the highest in the scale is, for the
most part, m.ade up of but a few sim.ple ideas, such
as the mind can take in and survey with ease. This
first general notion, when branched out into the dif-
ferent subdivisions contained under it, has in every one
of them something peculiar, by which they are dis-
tinguished among themselves ; insomuch that in de-
scending from the genus to the species, we alwavs
superadd som.e new idea, and thereby increase the
degree of composition. Thus the idea denoted by
the word/^wre, is of a very general nature, and coni-
posed of but few simple perceptions, as implying no
more than space every where bounded. But if v/e
descend farther, and consider the boundaries of this
space, as, that they m.ay be either lines or surfaces,
we fall into the several species of figure. For where
tiie space is bounded by one or more surfaces, we
O
106 'BUKCAN^s ELEMENTS
fj,ive it the Dame of a srAid figure ; but where the
boundaries arc lines, it is called zl jilain figure .
Sec. VI. — 'The Idea of the S/iecies formed by sujieradd-
ing the sjiecific Difference to the Genus.
In this view of things, it is evident, that the species
are formed by superadding a new idea to the genus ^
Here, for instance, the genus is circumscribed space.
If now to this we superadd the idea of a circumscrip-
tion by line, we frame the notion of that species of
figures which are called plain ; but if v.e conceive
the circumscription to be by surfaces, we have the
species of solid figures. This superadded idea is call-
ed the specific diiferc7ice^ not only as it sei-ves to di-
vide the sptciss from the gcnufi, but because, being
different in ai-1 the several subdivisions, v/e thereby
also distinguish the species one from anciher. And
as it is likewise that conception, Avhich, by being join-
ed to the general idea, completes the notion of the
c/ieciec ; hence it is plain, that the genus and specific
difference are to be considered as the proper and ccn-
biituent parts cf the species. If we trace the progress
of the mind still farther, and observe it advancing
through the inferior species, we shall find its manner
of proceeding to be always the same. For every
lower species is formed by superadding some new
idea to the species next above it ; insomuch, that m
descending the scale of our perceptions, the under-
standing passes through different orders of complex
notions, wliich become more and more complicated
lit every step it takes. Let us resume here, for in-
stance, the species of plain figures. They imply no
more than space bounded by lines. But if we take
in an additional consideration of the natm'e of these
lines, as, whether they are right or curves, we fall into
the subdivisions of plain figure, distinguished by the
names rectilinear, curvilinear and mixtilinear.
OF LOGIC. lor
Sec. Vn.— v-^^rf 271 all the inferior species by szcfieradd^
ing the specijic to the nearest gemis.
And here we are to observe, that though plain fig-
ures, when considered as one of those branches thai
ccme under the notion of figure in general, take the
name of a species ; yet compared with the classes of
curvilinear, rectilinear, and mixtilinear, into whicU
they themselves may be divided, they really become
a genus, of which the before mentioned subdivisions
constitute the several species. These species, in the
same manner as in the case of plain and solid figures,
consist of the genus and specific difference, as their
constituent parts. For in the curvilirisar kind, the
curvity of tiie lines bounding the figure, makes what
is called the s/iecijic difference ; to which if we join
the genus, which here is plain figure, or space cir-
cumscribed by lines, we have ail that is necessary
towai'ds completing the notion of the species. Vv e
are only to take notice, that this last subdivision, hav-
ing two genera above it, viz. plain Jlgure, arid ^figure
in general i the genus, joined with the specihc ditfer-
ence, in order to constitute the species 61 curvilinear^
is that which lies nearest to the said species. It is
the notion oi plain figure^ and not oi'Jigztre in general,
that, joined with the idea of ciii-vity^ makes up the
complex conception of curved-lined figures. For in
this descending sc-ale of our ideas — Fig^ire in general,
idain figures^ curve-lined figures — the two first are
considered as genera in respect to the third ; and the
second in order, or tliat vvhich stands next to the-
third, is called the nearest gciius. But now as it is this
second idea, v/hicli, joined with the notion of curvity,
forms the species of curve-lined figures ; it is plain,
that the third or last idea in the series, is made up of
the nearest gams and. specific diff'ercnce. This rule
108 DUNCAN'S ELEMENTS
holds invariably, however far the series is continued';
because in a train of ideas thus succeeding one anoth-
er, all that precede the last are considered as so ma-
ny genera, m respect of that last ; and the last itself
is always formed, by superadding the specific differ-
ence to the genus next it.
Sec. VIII. — The idea of o^n individual cmiiiosed of the
(oweat species and rMmeric difference..
Here then we have an universal description, appli-
cable to all our ideas, of whatever kind, from the high-
est genus, to the lowest species. For taking them in
order downwards from the said general idea, they
every where consist of 'i\\Q^ genus proxhnum^ and dif
ftrentia sjiecifica^ as logicians love to express them-
selves. But when we come to the lowest species of all,
comprehending in it only individuals, the superadd-
ed idea, by which these individuals are distinguished
one from another, no longer takes the name of the
fH^ecific difference. For here it serves not to denote
distinct species, but merely a variety of individuals,
each of v/hich, having a particular existence of its
own, is tiierefore nnmericailij different from"every oth-
er of the same kin<l. And hence it is, that in this
last case, logicians choose to call the superadded idea
by the name of the numerical (/?^f-re?!C(? ; insomuch
thict as the idea of a species, is made up of the near-
tst genus and specific diffire?ice^{s6 the idea of an in-
dividual consists of the lowest hpecibs oxiCt niuneric dif-
ference. Tkus the circle is a species of curve-iined
figures, and what we call the lowest species^ as com-
prehending under it only individuals. Circles in par-
ticular are dlstuiguished from one another by the
length and position of their diameters. The length,
tlierefore, and position of the diameter of a circle, is
uhat logicians cull tiie niunerical difference ; becau3<^
OF LOGIC. 109
these being given, the circle itself may be described,
and an individual thereby constituted.
Sec. IX. — Dejinitions to follow one another in train^
and pass through the same successive gradations as
our cornfiouyid ideas.
And thus we have endeavored to ti^ace, in the best
manner we are able, the progress of the mind in
compounding its ideas. It begins, Ave see, with the
most general notions, which, consisting of but a few .
simple notices, are easily combined and brought to-
gether into one conception. Thence it proceeds to
the species comprehended under this general idea,
and these are formed by joining together the genus
and sfiecijic difference. And as it often happens, that
these species may be still further subdivided, and run
on in a long series of continued gradations, producing
various orders of compound perceptions ; so all these
several orders are regularly and successively formed,
by annexing in ei'ery step, the sfiecific difference to
the nearest genus. When by this method of proce--
dure, we are come to the lowest order of all; by
joining the species and numeric difference^ we frame
the ideas of individuals. And here the series neces-
sarily terminates, because it is impossible any farther
to bound or limit our conceptions. This view of the
com.positicn of cur ideas, representing their ccnstitu-
ent parts in every^ep of the progression, naturally
points out the true and. genuine form of a definition..
For as deSnitions are no more tlian the. descriptions
of the ideas for which tlie terms denned stand ; and
as ideas are then described, when we enum.erate dis-
tinctly and in order, the parts of which they consist ;
it is plain, that by making our definitions foIlov\^ one
anotlier, according to tlie natural train of our concep-
tions, they will be su1:>ject to the same rules, and keep
pace '.yith the idea^' they describe,.
no DUNCAN'S ELEMENTS
Sec. X. — The form of a Definition in all the various'
orders of Cor.ccption.
As therefore the first order of our Gompoimd no-
tions, or the ideas that constitute the highest genera,
in the different scales of perception, are formed, by-
uniting together a certain number of simple notices ;
so the terms expressing these genera, are defined by
enumerating the simple 7ictices so combined. And as
the species comprehended under any genus, or tjie
complex ideas of the second order, arise from super-
adding the specific difference to the said general idea ;
so the definition of the names of the species is absolv-
ed, in a detail of the ideas of the sjiecifc difference^ con-
nected ivith the term of the g£nus. For the genus hav-
ing been before defineil, the term by which it is ex-
pressed stands for a known idea, and may therefore
be introduced into all subsequent definitions, in the
same manner as the names of simple perceptions. It
will nov/, I think, be sufficiently obvious, that the de-
finitions of all the succeeding orders of compound no-
tions, will every wliere consist of the term of the nearest
genus joined with an e^iumeration of the ideas that con-
ctitute the specif c difference ; and that the definition
of individuals unites the name of the lowest species, with
the terms by which we express the ideas of the numeric
difference.
Sec. XL — The logical method of definmg perfect in its
kind ;
Here then v/e have the ti-ue and proper fomi of a
definition, in all the various orders of conception.
This is that method of defining, w hich is commonly
called logical, and which, we see, is perfect in its kind,
inasmuch as it presents a full and adequate descrip-
tion of the idea, for which the term defined stands.
There are still two things worthy of observation, be-
OF LOGIC 411
fore we take leave of this subject. First, that the very
frame and contexture of these definitions, points out
the oiKler in which they ought to follow one another.
For as the name of the genus is admitted into a de-
scription, only in consequence of its having been be-
fore defined ; it is evident, that we must pass gradu-
ally through all the diiTerent orders of conception.
Accordingly, logicians lay itdo-vvn as a rule, that we
are to begin always with the highest genus, and car-
ry on the series of definitions regularly, through all
the intermediate genera and species, quite down to the
individuals. By this means our descriptions keep
pace with our ideas, and pass through the same suc-
cessive gradations ; insomuch, that the perusal of
them must excite those ideas in the understanding of
another, in the very order and manner in which they
are put together by the mind in its uniform advances
from simple to the most complicated notions. Now
this is the ti-ue and proper end of defining, and in-
deed the higiiest perfect!on of that art.
Sec. XII.— 'y^;i<i apjilicable to all words whatsoever ca^
fiabic of a dejlrdtion.
There is yet another thing to be observed on this
head, namely, that the form here prescribed, is appli-
cable to all vvords v/hatsoever, capable of a definition;
For as every term v/e use, must denote some idea,
either general or particular ; and as all our com.plex
notions relating to both these classes of perception
from the highest genus quite down to the individuals,
come v/ithin the rules of description here given ; it is
evident, that this paiticular manner of unfolding an
idea, may be extended to all the possible ccmplex
conceptions v/e can connect with ourv/ords. By the
rules therefore of this method, definitions may be ap-
plied to all terms standing for complex ideas ; aiad
112 DUNCAN'S ELEMENTS
as these, by what Ave have shown at large in the two
foregomg chapters, are the only definable articles of
speech ; it necessarily follows, that the directions
here given are universal, extend to ail particular in-
stances, and are alike applicable in ail languages. —
And thus at length, we have not only deduced that
peculiar form of a dennition which obtains among lo-
gicians, but shown it also to be perfect in its kind,
and to take in the whole compass of language.
BOOK II.
OF JUDGMENT, OR INTUITION.
CHAP. L
OF THE GHOUNDS OF HU3IAN JUDGMENT.
Sec. T. Intuition 7'esfiecta the relation between our I-
deas when they are immediately perceivable.
When the mind is furnished with ideas, its next
step in the way to knowledge is, the comparing these
ideas together, in order to judge of their -agreement
or disagreement. In this joint view of our ideas, if
the relation is such, as to be immediately discovera-
ble by the bare inspection of the mind ; the judg-
.jnents thence obtained are called ifituitive^ from a
word that denotes to look at: for in this case, a mere
attention to the ideas compared, suffices to let us see,
how far they are connected or disjoined. Thus, that
the whole is greater than any of its parts, is an intui-
tive judgment, nothing more being required, to con-
OF LOGIC. 113
vince ii5 of its truth, than an attention to the ideas
oiivhals ziidpart. And this, too, is tiie reason, why
v/e call the act of the mind forming these judgments
intuithn ; as it is indeed no more than an immediate
perception of the agreement or disagreement of any
tvvo ideas.
Sec. II. — Exfierience and Testimony the Ground of
judging as to Tacts.
But here it is to be observed, that cur knowledge
cf this kind, respects only our ideas, and the rela-
tions between them, and therefore can serve only as
a foundation to such reasonings, as are employed ia
investigating these relations. Nov/ it so happens,
that many of our judgments are conversant about
facts, and the real existence of tilings which cannot
be traced by the bare contemplation of our ideas. It
does not follow, because I have the idea of a circle
in my mind iliDl therefore a figure answering to that
idea, has a real existence in nature. I can form to
myself the notion of a centaur, or golden mountain,
but never imagine on th.at account, that either of them
exists. Vv hat then are the grounds of our judgments,
in relation to facts ? I answer, these two : exjiericnce
and testimonij. By ejcperience we are iniorm-ed of the
existence of the several objects whicli surround us,
and opei^te upon cur senses. Testlincny is of a
wider extent, and reaches not only to objects beyond
the present sphere of our observation, but also to
facts and transactions, vrhich, being now past, and
having no longer any existence, could not, without
tnis conveyance, have fallen under our cognizance.
Sec. III. — Three Fc:mdatio'ns of human Judgment^ viz.
1. Lituition^ the Ground of scientifcal knowledge ;
Here then we have three foundations of human
judgment, from which the v^diole svsteni of our laaowl-
P
114 DUNCAK^s ELEMENTS
edge may with ease and advantage be deduced. First,
inndtion, wiiich respects our ideas themselves, and
their relations, and is the foundation of that species
of reasoning v/hich we call demonstration. For what-
ever is deduced from our intutive perceptions, by a
clear and connected series of proofs, is said to be de-
monstrated, and produces absolute certainty in the
mind. Kence the knowledge obtained in this man-
ner, is what wc properly term science ; because, in
every step of the procedure, it carries its own evi-
dence along with irt, and leaves no room for doubt or
hesitation. And what is highly wortliy of notice ; as
the truths of this class expressthe relations between
our ideas, and the sam.e relations must ever and inva-
riably subsist betv/een the same ideas, our deduc-
tions, in the way of science, constitute what we call
eternal, necessary, and immutable truths. If it be
true, that the whole is equal to all its parts, it must
be so unchangeably ; because the relations of equal-
ity being attached to the ideas themselves, must ever
intervene where the same ideas are compared. Of
this nature are ail the truths of natural religion,
morality, and mathematics ; and in general whatever
may be gathered from the bare view and considera-
tion of our ideas.
Sec. IV.--2. ErheriencetheGrortndof our Knowledge
of the Povjers and Qualities of Bodies.
The second ground of human judgment is experi-
ence ; from Avhich we infer the existence of those
objects that surround us, and fall under the immedi-
ate notice of our senses. When we see the sun, or
cast our eyes towards a building, v/e not only have
ideas of these objects within ourselves, but ascribe
to them a real existence out of the m^ind. It is also
by the information of the senses, that we judge of.
OF LOGIC. 115
the qualities of bodies ; as wherx ^ve say thrtt snow
is white, fire hot, or, steel hard. For as we are vrhol-
ly unacquainted with the internal structure and con-
stitution of the bodies that produce these sensations
in us, nay, and are unable to trace any connexion be-
tween that structure and the sensations themselves,
it is evident that we build our judgments altogether
upon observation, ascribing to bodies such qualities
as are ansv\'erab]e to the perceptions they excite in
us. But this is not the only advantage derived from
experience, for to that, too, are v.-e indebted for all
our knowledge regarding the co-existence of sensible
qualities in objects, and the operations of bodies one
upon another. Ivory, for instance, is hard and elast-
ic ; this we know by experience, and indeed by that
alone. P'or being altogether strangers to the true
nature both of elasticity and hardness, we cannot, by
the bare contemplation of our ideas, determine hew
far the one necessarily implies the other, lor whether
there may not be a repugnance between them. But
when we observe them to exist both in the same ob-
ject, we are then assured from experience that they
are not incompatible ; and when we also find, that a
stone is hard and not elastic — and that air, though
elastic, is not hard — we also conclude, upon the same
foundation, that the ideas are not necessarily conjoin-
ed, but may exist separately in diiTerent objects. In
like manner, with regard to the operations of bodies,
one upon another, it is evideTit, that our knowledge
this way is all derived from obser-y-ation. .dqua regia
dissolves gold, as has been found by frequent trial ;
nor is there a.ny other vv'ay of arriving at the discove-
ry. Naturalists may tell us, if they please, that the
parts of aqua regia are of a texture apt to insinuate
between the corpuscles of gold, and thereby loosen
and shake them asunder. If this is a true account of
i IC DUNCAN'S ELEMENTS
the matter, I believe it will, notv/ithstanding, be al-
lowed, that our conjecture, in regard to the conforma-
tion of these bodies, is deduced from the experiment,
and not the experiment from the conjecture. It was
i>ot from, any previous knowledge of the intimate
structure of ag-ua rsgia and gold, and the aptness of
tlicir parts to act or be acted upon, that we came by
the conchision above-mentioned. The internal con-
btilULion of bodies is in a manner wholly unknov\m to
us : and could v/e even surmount this diiiiculty, yet
as the separation of the parts of gold imxplies some-
thiii^ like an active force in the menstruum, and Ave
c.re unable to conceive how it comes to be possessed
of this activity ; the effect must be owned to be alto-
gether beyond our comprehension. But when, re-
peated trials had once coniirm.ed it, insomuch that it
was admitted as an established truth in natural kno'^vl-
edge, it was then easy for men to spin out theories of
their own invention, and contrive such a structure of
par;;s both [ovgold and agua regia, as would best serve
to explain the phenomenon, upon the principles of
tnat system of philosophy they had adopted. I mxight
easily shovv^ from kinumeraole other instances, hov/
much our knowledge of the mutual action of bodies
depends upon observation. The bite of a viper will
hill. Plants are some sahitary, others noxious. Fire
dissolves one body, and hardens another. These are
truths generally knov/n ; nor is it less evident tliat v/e
owe their discovery wholly to experience.
Sec. v.- — IVhy mamj use/id Lroentions o'-ive their Birth
to Chance.
And hence it is easy to account for what to some
wri»:ers lias appeared a very great paradox ; that ma-
ny of the mobt important inventions in human life
OF LOGIC. iir
have taken their rise from chance, and instead of
coming out of the schools of philosophers are for the
most ascribed to men of no figure in the common-
wealth of learning. Sowing, planting, the use of
compass, and such like, are not deductions of human
reason, but discoveries which ovve their birth to ob-
servation and trial. No wonder, therefore, if these
inventions derived their beginning from such, as, be-
ing engaged in the active and busy scenes of life,
were more in the way of those experiments which
lead to discoveries of this nature. And here, as the
particular callings and professions of men, and oft-
times chance, has a great ascendant, it need not seem
strange, if some of the most useful arts in society
appear to have had an original purely casual.
Sec. Yl.-^A'atura! Ktio^vledge^ from the Grounds on
=<.^'iiich it rebts^ aptly termed expenmental Philosophy .
From Vv'hat lias been said, it is evident, that as in-
tuition is the foundation cf what we call scientiftcal ■
knovvledge, so is experience of natural. For this last
being wholly taken up with the objects of sense, or
those bodies that constitute the natural Vv^orld — and
their properties, as far as we can discover them, be-
ing to "be traced only by a long and painful series cf
observations ; it is apparent, that in order to im.prove
tliis branch of knowledge, we must betake ourselves
to the method cf trial and experiment. According-
ly, v.'e find, that while this was neglected, little ad-
vance was m.adein the philosophy of nature ; where-
as a contrary proceeding has enriched the present
age with many valuable discoveries ; insomuch that
natural knovdedge, in allusion to the foundation on
"which it stands, has been very aptly called expert-
mental philosophy.
lis- DUNCAN'S ELEMENTS
Sec. VIL — Though much of our Knowledge of Body
depends on Testimony^ yet Extierience is the ultimate
Foundation of it.
But though experience is vvhat we may term the
immediate foundation of natural knowledge, yet with
respect to particular persons, its influence is very
narrow and^ confined. The bodies that surround us
are numerous ; many of them lie at a great distance ;
and some quite beyond our reaci-u Life too is short,
and so crowded with cares, that but little time is left
for any single man to employ himself in unfolding
the mysteries of* nature. Hence it is necessary to-
admit many things upon the testimony of others,
which, by this means, becomes the foundation of a
great part of our knowledge of body . No man doubts
of the power of acqiia regia to dissolve gold, though
perhaps he never himself made the experiment. In
these, therefore, and such like cases, we judge of the
facts, and operations of nature, upon the mere ground
of testimony. Hovv'ever, as v/e can ahvays have re-
course to experience, where any doubt or scruple
arises, this is justly considered as the true foundation
of natural philosophy, being indeed the ultimate sup-
port upon Yv^hich our assent rests, and whereto we
appeal, when the highest degree of evidence is re-
quired.
Sec. VIIL — 3. Testimony the Ground of Historical
Knoivledge.
But there are many facts that v/ill not allow of an
appeal to the senses, and in this case testimony is the
true and only foundation of our judgments. All hu-
man actions, of whatever kind, when considered us
already past, are of the nature here described ; be*
cause having ho^y no longer any existence, both the
r
OF LOGIC. 11^
facts themselves, and the circumstances attending
them, can be known only from the relations of such
as had sufficient opportunities of arriving- at the truth.
Testimony^ therefore, is justlv accounted a third
ground of human judgment : and as from the other
two we have deduced sdmt'fical and natural knowl-
edge, so may we from this derive historical ; by which
I v.ould be understood to mean, not merely a knowl-
edge of the civil transactions of states and kingdoms,
but of all facts whatsoever, where testimony is the ul-
timate foundation of our belief
Sec. IX. — Tilt second Operation of the Mind^ commori-
ly extended beyond Intuition..
Before I conclude this chapter, it will be necessary
to observe, that though the second operation of the
mind, properly speaking, extends not beyond intuitive
perceptions, yet logicians have not confined them-
selves to so strict a view of it ; but calling it by the
name judgment^ thereby denote ail acts of the mind,
W'here only tv%'o ideas are compared, v^^ithout the im-
mediate interposition of a third. For when the mind
joins or separates two ideas, though perhaps this is
done in consequence of a train of previous reasoning,
yet if the understanding proceeds upon established
notions, without attention to that train of reasoning,
its determinations are still considered as acts of judg-
ment. Thus, That God created the universe^ that
vien are accountable for their actions,^ are frequently
mentioned by logicians, as instances of the mind
judging. And yet it is apparent, that these judg-
ments are by no means of the kind v/e call intuitive ;
nay, that it requires much exercise of the reasoning
fciculty, before a man can trace their connexion with
the perceptions of that name. I could in the same
manner easily show, that even our judgments of ex-
120 DU^XAN's ELEMENTS
perlence and testimony, v/hen pursued to their source,
derive all their power of persuasion, from being link-
ed with intuitive truths. But I shall wave this en-
quiry for the present, as being of a nature too subtile
for a work of this kind. The remark itself, howev-
er, was needful, as well to illustrate the proper dis-
tinction between the powers of the understanding, as
to explain the reason, why in this part of logic, we
extend the second operation of the mind beyond those
limits, that in strictness of speech belong to it. Let
us now proceed to consider a little more particularly
tlie nature and variety of these our judgments.
CHAP. n.
OF AFFIRMATIVE AND NEGATIVE PROPOSITIONS.
Sec. I. The subject cmd predicate cf a Proposition
exjilaiiicd.
V V HiLE the comparing of our ideas is considered
merely as an act of the mind, assembling them to-
gether, and joining or disjoining them according to
tiie result of its perceptions, v/e call it judgment ; but
when our judgments are put into words, they then
bear the name qi firopo&iiions. A proposition, there-
fore, is a sentence expressing some judgment of the
mind, v.diereby tv/o or more ideas are aairmed to
a;^ree or disagree. Now, as our judgments include
at least two ideas, one of which is affirmed or denied
of the other, so must a proposition have terms' an-
swering to these ideas. The idea, of which v/e af-
firm or deny, and of course the term expressing that
OF LOGIC. 121
idea, is called the subject of the proposition. The
idea affirmed or denied, as also the term answering
it, is called the Jiredicate. Thus in the proposition,
God is omnifiotent : God is the subject, it being of
him that we affirm omnipotence ; and o?nnipotence is
the predicate, because we affirm the idea, expressed
by that word to belong to God.
Sec. ll.--T/ie Cojmla, ilfc.
But as in propositions, ideas are either joined or
disjoined ; it is not enough to have terms expressing
tliose ideas, unless v/e have also some words to de-
note their agreement or disagreement. That word
in a proposition, v/hich connects two ideas together,
is called the cofiula ; and if a negative particle be an-
nexed, we thereby understand, that the ideas are dis-
joined. The substantive ~oerb is commonly made use
of for the copula, as in the above-mentioned proposi-
tion, God is omninotent ; where it represents the co-
pula, and signifies the agreement of tiie ideas God
and omnifiotence. But if we mean to separate tv/a
ideas, then, besides the substantive verb, we must
also use some particle bf negation, to express this
repugnance. The proposition, -nian is not fierfect^
may ser^^e as an example of this kind, where the no-
tisn of perfection being removed from the idea of
man^ the negative particle, not^ is inserted after the
copula, to signify the disagreement between the sub-
ject and predicate.
Sec. III. — Pr oppositions sometimes ejc/iressed by a sin-
gle 'ivord.
Every proposition necessarily consists of these
three parts ; but then it is not alike needful, that
they be all severally expressed in words ; because
the copula is often included in the term of the predi-
cate ; as when we say, he sits ; which imports the
Q
122 DUNCAN'S ELEMENTS
same as he is sitting. In the Latin languages a single
Avord has often the force of a whole sentence. Thus
ambulat is the same, as ilk est ambulans ; amo^ as ego
sum ainans ; and so in innumerable other instances ;
by which it appears, that we are not so much to re-
gard the number of woi^s in a sentence, as the ideas
ihey represent, and the manner in which they are
put together. For whenever two ideas are joined or
disjoined in an expression, though of but a single
>vord, it is evident, that vre have a subject, predicate,
a;)d copula, and of consequence a complete propo-
i,ition.
Sec. IV. — affirmative and .Negative Propositions.
When the mind joins tw^o ideas, we call it an af-
firmative judgment ; when it separates them a neg-
ative ; and as any two ideas com.pared together,
must necessarily either agree or not agree, it is evi-
dent, that all cur judgments fall under these two di-
visions. Hence, likewise, the proposition expressing
these judgments, are all either affirmative or nega-
tive. An affirmative proposition connects the predi-
cate with the subject, as, a stone is heavy : a nega-
tive proposition separates them, as, God is not the au-
thor of evil. Affirmatio7i^ therefore, is the same as
joining two ideas together ; and this is done by means
of the copula. JVegation., on the contrary, marks a
repugnance betv/een tlie ideas compared ; in which
case a negative particle must be called hi, to show
that the connexion included in the copula does not
take place.
Sec. V. — JVhen the negative particle serves to dzsJoi?i
ideas.
And hence we see the reason of the rule common-
ly laid down by logicians, that in all negative propo-
OF LOGIC. 123
sitions, the negation ought to affect the copula. For
as the copula, when placed by itself, between the sub-
ject and the predicate, manifestly binds them tog-eth-
er; it is evident, that in order to render a proposition
negative, the particle of negation must entvii^L -n
such manner, as to destroy this union. In /word,
then only are two ideas disjoined in a proposition,
when the negative particle may be so referred to the
copula, as to break the afarmation included in it, and
undo that ccnne^don it would otherwise establish.
When we say, for instance, no man is fitrf^ct ; take
av/ay the negation, and the copula of itself plainly
unites the ideas in the proposition. But as this is the
very reverse of what is intended, a negative mark is
added, to show that this union does not here take place.
The negation, therefore, by destroying the effect of
the copula, changes the very nature of the proposition,
msomuch that instead of binding two ideas toirether, it
denotes their separation. On the contrary^ in this
sentence, the man vjho departs not from an upright be-
havior, is beloved of God ; the predicate, beloved of
God, is evidently affirmed of the subject, an upiright
man ; so that notvv-ithstariding the neeative particle,
the proposition is still affirmative. "Xhe reason is
plam ; the negation here affects not the copula, but
making properly a part of the subject, serves, with
other terms in the sentence, to form one complex idea,
oi v/hich the predicate, beloved of God, is directly af-
firmed. This, perhaps, to some may annear a mere
logical refinement, contrived to justifv the scholastic
rule lor distinguishino; between affirmative and nega-
tive propositions. But if it be considered, that this
distinction is of great importance in reasoning, and
cannot m many cases be made with certainty, but by
means of this criterion here given, the reader will see
sufficient reason for my taking so much pains to il-
lustrate it.
124 DUNCAN'S ELEMENTS
Sec. VI. — Hoiv a Copula comes to be a part of a nega-
tive proposition.
Perhaps it may still appear a mystery, how a copu-
la can be said to be a part of a negative proposition,
whose proper business it is to disjoin ideas. This
diiFiculty, however', will vanish, if vre call to mind, that
every judgment implies a direct affirmation, and that
this affirmation alone niakcs the true copula in a pro-
position. But as our affirmations are of tv/o kinds,
vi^:. either of agreement or of disagreement, between
the ideas compared ; hence there is also a twofold ex-
pression of our judgments. In the case cf agreement,
the copula alone suffices ; because it is the proper
mark whereby we denote an identity or conjunction
cf ideas. But where perceptions disagree, there we
must call in a negative panicle : and this gives us to
understand that the affirmation imxplied in the copula,
is not of E-ny connexion between the subject a.nd pre-
dicate, but of their mutual opposition and repugnance.
CHAP. III.
GF UNIVERSAL AND PARTICULAR PROPOSITIONS.
Sec. I. — Diviaion of Propositions into Universal and
Particular.
X KE next considerable division of propositions, is
into univercul and particular. Our ideas, according
to what lias been already observed in the first part,
;tre all singular, as they enter the mind, and represent
individual objects. But as by abstraction v/e can ren-
der them universal, so as to comprehend a v/hole cJass
uf things, and sometimes several classes at once ;
hence the terms expressing these ideas must be in
OF LOGIC. 125
like manner universal. If, therefore, we suppose any
general term to become the subject of a proposition,
it is evident, that whatever is affirmed of the abstract
idea belonging to that term, may be affirmed of all the
individuals to which that idea extends. Thus when
we say, men are mortal i we consider mortality, not as
confined to one or any number of particular men, but
as what may be giiirmed v/ithout restriction of the
vrhcie species. By this means, the proposition be-
comes as general as the idea which makes the sub-
ject of it, and indeed derives its universality entirely
from that idea, being more or less so, according as
this may be extended to more or fewer individuals.
But it is further to be observed of these general terms,
that they sometimes enter a proposition in tlieir full
latitude, as in the example given above ; and some-
times appear witli a mark of limitation, in this last
case, we are given to understand, that the predicate
agrees not to tlie whole universal idea, but only to a
part of it ; as in the proposition, some men are iinse :
for here wisdomx is not affirmed of every particular
man, but restrained to a few of the human species.
Sec. II. — Prepositions traversal vjhere the subject is
sOy without a mark ojrestj'iction.
Nov; from this different appearance of the general
idea, that constitutes the subject of any judgment,
arises the division of propositions into uni-oersal and
fiarticidar . An vni-jer-^al proposition 'is that, where-
in the subject is some general term, taken in its full
latitude, insomuch that the predicate agrees to all the
individuals comprehended under it, if it denotes a
proper species ; and to all the several species and
their individuals, if it marks an idea of a higher or-
der. The words, c//, every, no, none, Sec. are the
proper signs of this universality ; and as they seldom
I2G DUNCAN'S ELEMENTS
fail to accompany general truths, so they are the
most obvious criterion whereby to distinguish thein.
jill animals have a ponver of beginning motion. This
is an universal proposition ; as we know from the
word alU prefixed to the subject ctz/wg/, which denotes
that it must be taken in its full extent. Hence the
power of beginning motion may be amrmed of all the
several species of animals ; as of birds, quadrupeds,
insects, fishes, Sec. and of all the individuals of which
these different classes consist, as of this hawk, that
horse, and so for others.
Sec. III. — Profiositions particular nvhere some univer-
sal Subjects appear iri^h a Mark of Limitation,
K particular proposition has in like manner some
general term^ for its subject, but with a mark of limi-
tation added, to denote, that the predicate agrees on-
ly to some of the individuals comprehended under a
species, or to cne or m^ore of the species belonging
to any genus, and not to the whole universal idea. —
Thus, sov.ie stones are heavier than iron ; some men
have an uncommon share of prudence. In the last of
these propositions, the subject, come men^ implies on-
ly a certain number of individuals, comprehended un-
der a single species. In the former, where the sub-
ject is a genus, that extends to a great variety of dis-
tinct classes, some stones may not only imply any
number of particular stones, but also several v/hole
species of stones ; inasmuch as there may be not a
fev.^, with the property there described. Hence we
see, that a proposition does not cease to be particu-
lar, by the predicate's agreeing to a wdicle species,
unless that species, singly and distinctly considered,
makes also the subject of which vre affirm or deny.
For if it belongs to some genus, that has other spe-
cies under it, to which the predicate does not agree ^
OF LOGIC. 127
it is plain, that where this genus is that of which we
affirm or deny, the predicate agreeing- only to a pan:
of it, and not to the whole general idea, constitutes
the proposition particular.
Sec. IV. 4" sure a?2d infallible Criterion^ ivhereby to
distinguish bet-iVeen urdversal and fiarticiUar jPro/io-
sitions.
Here then, we have a sure and infallible mark,
whereby to distinguish betvv^een universal and partic-
ular propositions. Where the predicate agrees to
all the individuals comprehended under the notion of
the subject, there the proposition is universal ; where
it belongs only to some of them, or to some of the
species of the general idea, there the proposition is
particular. This criterion is of easy application, and
much safer than to depend upon the common signs
of c//, every, some, none, Sec. because these being dif-
ferent in diiterent langu-ges, and often varying in
their signification, are very apt in many cases to mis-
lead tile judgment. Thus if we say, ^/Z the soldiers
nvhen dranvn ufi, fjvmed a square of c hundred men a
side : it is evident that the predicate cannot be af-
firmed of the several individuals, but of the whole
collective idea of the subject ; whence, by the rule
given above, the proposition is not universal. It is
true, logicians lay down many observations, to ena-
ble us to distinguish aright on this head: but if the
criterion here given be duly attended to, it v.'iil be of
more real^ service to us than an hundred rules. For
It IS infallible, and may be applied ^ith ease ; where-
as the directions, which we meet with in treatises of
logic, being drawn for the most part from the analo-
gy oi language, and com.m.on fcnns of speech, arc
not only burdenscme to the rnemoiy, but often very
doubtful and uncertain in their application.
32S DUNCAN'S ELEMENTS
Sec. v.— Singular Propositions contained U7ider the
head of particulars ,
There is still one species of propositions that re-
mains to be described ; and which the more deserves
our notice, as it is not yet agreed among logicians,
to wliich of the two classes mentioned above, they
ought to be referred. I mean 5W5''7'/ar propositions ;
or those where the subject is an individual. Of this
nature are the following : Sir Isaac J\''t'voton was the
inventor of jiuxions ; this book contains many v.ssful
truths. What occasions some difficulty, as to the
proper rank of these propositions, is, that the subject
being taken according to the whole of its extension,
they sometimes have the same effect in reasoning, as
universals. But if it be considered, that they are, in
truth, the most limited kind of particular proposi-
tions, and that no proposition can, v/ith any propriety,
be called universal, but where the subject is some
universal idea ; v/e shall not be long in determining
to which class they ought to be referred. When we
say, some books contain useful truths^ the proposition is
pralicular ; because the general term appears vdth a
mark of restriction. Ifj' therefore, we say, this book
contains useful truths ; it is evident, that the proposi-
tion must be still more particular, as the limitation,
implied in the word, this^ is of a more confined na-
ture, than in the former case. 1 knov/ there are in-
stances, where singular propositions have the same
effect in reasoning, as universals ; yet is not this, by-
reason of any proper universality, belonging to them ;
but because the conclusion, in such cases being al-
ways singular, may be proved by a middle term
which is also singular ; as I could easily demonstrate,
were this a proper place for entering Into a discussion
#f that nature.
Sec. VI.— 77:^ Fovrfold Division of Proptsitzons.
We see, therefore, that all propcsitions are either
affirmative ov ne gat i-ve ; nor is it less evident, that in
both cases, they be universal or particular. Hence
arises that celebrated fourfold division of them, into
universal affirmative^ and universal negative ; particv-
lar affiirrnative^ and partinuar negative ; which ccm-
preliends, indeed, all their varieties. The use of this
method of distinguishing them vrill appear more ful-
ly afterwards, when we come to treat of reasoning
and syllogism.
CKAP. IV.
' OF ABSOLUTE A1<.'D CONDITIONAL PnOrOSITIOXS.
Sec. I. — Distinction cj Qualities into Essential and Ac-
cidental.
X HE objects, about which we ?.re chiefly conversant
in this world, are all of a nature liable to change.—
"What may be ciffirmed of them at one time cannot
often at another ; and it makes no small part of our
knowledge to distinguish rightly these variations, and
trace the reasons upon which they depend. For it is
observable, that amidst all the vicissitudes of nature,
some things remain constant and invariable ; nor are
even the changes to vrhich we see others liable, ef-
fected, but in consequence of uniform and steady
laws, vv'hich, when kncvrn, are sufficient to direct us
in our judgments about them. Hence philosophers,
in distinguishing the objects of our perception into
various ckcsses, have been very careful to note, that
some properties belong essentially to the general
idea, so as not to be separable from it but by desrtoy*
ing its very nature ; while others are only accidental,
R
130 DUNCAN'S ELEMENTS
and may be affirraed or denied of it, in dilTerent cir-
cumstances. Thus, solidity, a yellov/ colour, and
great weight, are considered as essential qualities of
gold ; but whether it shall exist as an uniform, con-
joined mass, is not alike necessary. We see that by
a proper menstruum, it may be reduced to a nne
powder ; and that intense heat will bring it into a
state of fusion.
Sec. II. — Hence a cor.siderable Diversity in our Man-
nsr of judging,
Nov,', from this diversity in the several qualities of
thing's, arises a considerable difference as to theman-
ner of our judging about them. For in this first
place, all such properties, as are inseparable from
objects, when considered as belonging to any genus
or species, are affirmed absolutely and without re-
serve of that general idea. Thus \\q say, gold is ve-
ry roeighiij ; a stone is hard ; animals have a p.ov.ier of
^rlf'inotion. But in the case of mutable or accidental
ciualities, as they depend upon some other consider-
ation, distinct fi'om the general idea ; that also m.ust
be taken into the account, in o"der to form an accu-
rate judgment. Sliould v/e affirm, for instance, of
some stones, that they are very susceptible of a roll-
ing motion ; the proposition, while it remains in this
general form, cannot with any advantage be introduced
into our reasonings. An aptness to receive that mode
of motion Rows from the figure of the stone ; which,
as it may vary infinitely, our judgment then only be-
comes applicable and determinate, when the particu-
lar figure, of which volubility is a consequence, is al-
so taken into tiie account. Let us then bring in this
other consideration, and the proposition will run as
f^^lows : stones of a shhencal form are easily put irJo
a rolling motion. Here, v^e see the condition upon
OF LOGIC. 151
Avhich the predicate is amrmed, aiid therefore knew
III Avhat particular cases the propcsiticn may be ap-
plied.
Sec. III. — ^JV/iich gives rise to the division of Prof io-
siiions into Absolute aiid Conditional.
This consideration of propositions, respecting- the
mann^^r in which the predicate is affirmed of the sub-
ject, gives rise to tlie division of them into abhclute and
condiiioiud. Absolute propositions are those, wherein
we affirm some property inseparable from the idea of
the subject, and which, therefore, belongs to it in all
possible cases ; as, God is infinitehj ivise : virtue tends
to the uUimate hapjiiness of man. But where the pre-
dicate is not necessarily connected with the idea of
the subject, unless upon some consideration distinct
from that idea, there the proposition is called con-
ditional. The reason of the name is taken from the
supposition annexed, which is of the nature of a con-
dition, and may be expressed as such. Thus j if a
btojie is exposed to the rays of the iim^ it =:vill contract
some degree of heat. If a river runs in a very d.tciin-
ing cliannd^ its rafddity ^tvill constantly increase.
fcec. IV. — The great i?rp.ortance rf this division, as it
renders Prepositions determinate ;
There is not any thing of greater im.pcrtance in
philosophy, than a due attention to this division of
propcsiuons. If we are careful never to affirm things
absolutely, but where the ideas are inseparably con-
joined ; and if^ in our other judgments, we distinctly
mark the cohditions w^hich determine the predicate
to belong to the subject ; we shall be the less liable to
mistake, in applying general truths to the particular
concerns of human hfe. It is ov.ing to the exact ob-
servance of this rule, that mathematicians have been
ir.2 DUNCAWs ELEMENTS
so happ3^ in their discoveries ; and that what they de-
iiionstrate cf magnitude in general, may be applied
vvlch ease in all obvious occurrences.
Sec. V. a?id reduces thsm from particulars to generals,.
The truth of it is, particular propositions- are then
known to be true, when ^ve can trace their connexion
v.ithuniversals: and it is, accordingly, the great busi-
ness of science, to find out general truths, that may
be applied with safety in all obvious instances. Now
tl^e great advantage arising from determining with
care the conditions upon which one idea may be af-
nrm.ed or denied of another^ is this ; that thereby par-
ticular propositions reaily become universal, m.ay be
introduced with ceitainty into oiu' reasonings, and
serve as standards to conduct and regulate our judg-
ments. To illustrate this by a familiar instance : if
we say, some loater acts very forcibly ; the proposition
is particuiai' : and as the conditions, on which this
forcible action depends, are not mentioned, it is as yet
uncertain in what cases it may be applied. Let us
then supply these conditions, and the proposition will
run thus ; rjciter coi:rveycid in sujjicient quantity along
u steeti descent^ acts ucry forcibly.. Here we have an
universal judgment, inasmuch as the predicate,y^/Tr-
bi: aciio:iy may be ascribed to all water under the cir-
cumstances mentioned. Nor is it less evident, that
the propositio:! in this nev/ form h of easy application i
and in fact we fir.d, that men do a.pply it in instances
v.-here the forcible action of water is required ; as in
corn-mills, and many other worhs of art. Thus v/e
see, in what manner v/e are to proceed, in order ta
arrive at urdversal truths, which is the great end and
aim of science- And indeed, would men take the
same care, duly to express the conditions on v/hicli
fbey affii-m and deny, as niathcmadcians do* in tho^e
OF LOGIC. 13^5^
theorems which they term hypoihetical, I doubt not,
but we m)o;ht be able to deduce many truths, in other
parts of pralosophy, with no less clearness, force and
perspicuity, th:in has hitheito been thought peculiar to
the science of aaantity.
CHAP. V.
OF SIMPLE AXD COMPOUND PROPOS ITIC>f S .
Sec. I. — Division ef Propo-iitions into Sinifile and
Ccmjiound.
XT
Hitherto we have treated propositions, v.'here
cniy tv/o ideas are compared together. These are, in^
the general, called sivihlc ; beca.use, having but one
subject and one predicate, they are the effect of a,
simple judgment that admits of no subdivision. But
if it so happens, thai: several ideas oiler themselves,
to our thoughts at once, whereby v/e are led to anirni
the same thing of different objects, or different things,
ofthe same object ; the propositions, expressing these.
judgments, are called co'mjiound : because they may
be resolved inJio as many others as there are subjects
or predicates in the vrhcle complex determina-tion of
the mind. Thus, God is ivfinitely nvise and ir^initciy
poweyfid : here there are tv\'o predicates, ir^finiie wis-
dom and infinite poizcr^ both aflirmed of the same sub-
ject ; and accordinrily, the proposition m.ay be resolv-
ed into two others, anirming these predicates several-
ly. In like manner, in the proposition, ndther kin^?
n<jr fieafile arc exempt from dsaiJi^ the predicate is de~
nied of both subjects, and may therefore be separated
from them, indistinct propositions.. Nor is it less,
evident, that if a complex judgment consists of sever-
al subjects and predkatesj it may be resolved into ois.
i
1 34 DU^X AN's ELEI\!ENTS
many simple propositions as are the number of dif'
ferent ideas compared together. Riches and honors
are apt to elate the inind^ and increase the number of our
desires. In this judgment, there are two subjects and
two predicates : and it is at the same time apparent,
that it may be resolved into four distinct propositions.
Riches are apt to elate the mind. Riches are apt to in-
crease the number of our desires. And so of honours.
Sec. II. — The proper Xotion of a Comfiound Proposi-
tion ascertained.
Logicians have divided these compound proposi-
tions into a great many different classes ; but in my
opinion, not with a due regard to their proper defini-
tion. Thus conditionals^ casuals., relatives., (Jfc. are
mentioned as so m^any distinct species of this kind,
though in fact they are no more than simple proposi-
tions. To give an instance of a conditional : If a
stone is ejrpcscd to the rays of the S2in, it nvill contract
some degree of heai. Here Ave have but one subject
and one predicate ; for the complex expression, A
itone exposed to the" rays of the sun., constitutes the
proper subject of this proposition, and is no more than
one determinate idea. The same thing happens in-
easuals. Rehoboam r^as unhappy^ because he followed
evil counsel. I deriV not, that there is here an a.ppear-
ance of tv/o propositions arising from the complexity
of the expression ; but v/hen we come to consider the
matter more nearly, it is evident that we have iSut a
single subject and predicate. — The pursuit cfevilcoun-
sel brought misery upon Rehcboam. It is not enough,
therefore, to render a proposition compound, that the
subject and predicate are complex notions, requiring
ivometimes a whole sentence to express them : for in
tiiis case, the comparison is still confined to tw^o ideas,
and constitutes what we call u simple judgment. But
OF LOGIC. 135
v.here there are several subjects or predicates, or
both, as the aiiinnation or negation may be alike ex-
tended to them alljihe proposition, expressing such a
judgment, is truly a ccilection of as many simple
ones, as there are different ideas compared. Contin-
ing' ourselves, therefore, to this more strict and just
notion of compound propositions, they are all reduci-
ble to tv.'o kinds, viz. copulatives and disjunctives.
See. III. — Coivp.ound Propositions either Copuiative^
A copulative proposition is, where the subjects and
predicates are so linked lo.^ether, that they may be
all severally affirmed or denied one of another. Of
this nature are the examples of compound proposi-
tions given above. Riches and honors are apt to elate
the ?nind^and increase the number of our desires. .Yei-
ther kings nor people are exempt from death. In the
first of these, the two predicates may be affirmed sev-
erally of each subject, whence we hav^ four distinct
propositions. The other furnishes an example of the
negative kind, where. the same predicate being dis-
joined from both subjects, may be also denied of them
in separate propositions.
Sec. IV.— Or Disjimctive.
The other species of compound prepositions are
those called disjunctives ; in vrhich, comparing sev-
eral predicates with the same subject, we a-ffirm.,thaL
one- of them necessarily belongs to it, but leave the
purt*:uiar predicate undetermined. If any one, for
example, says : This ivorld 'either exists cf itself, or is
IS
tjie Kvdrk cf some all-tvise and po'iverful cause; it
evident, that one of the two predicates m^ust belong
to the world ; but as the proposition determines not
which, it is therefore of the kind we call dJsjunctive.
Such, too, are the folloviing: The sun either moves
.ir>5 DUNCAN'S ELEMENTS
round the earth,, or is the centre about tvhick the earth
revolves. Friendshifi finds men cqua^ or makes them so.
It is the nature of all propositions of this class, sup-
posing them to be exact in point cf form, that upon
determining the particular predicate, the rest are of
course to be removed ; or if all the predicates but
one are removed ; that one necessarily takes place.
Thus, in the example above, if we- allow the world to
be the work of some wise and powerful causp, we of
■course deny it to be self-sxistent ; or if we deny it to
be self-existent, we must necessarily admit that it
was produced by some wise and powerful cause. —
Now this particular manner of linking the predicates
together, so that the establishing one displaces all the
rest— or the excluding all but one necessarily estab-
lishes that one—- cannot otherwise l?^fiected than by
means of disjunctive particles. And hence it is, that
propositions of this class take their names from these
particles, which m.ake so necessary apart of them,
and indeed, constitute their very nature, considered
as a distinct species. But I shall reserve what far-
ther might be said on this head, till I come to treat of
reasoning, where the great use and importance of
disjunctive propositions will better appear.
CHAP. VI.
OF THE DIVISION OF PROPOSITIONS INTO SELF-EVI-
DENT AND DEMONSTRABLE.
Sec. I. — Design of this Chajiter.
l\s we arc soon to enter upon the third part of logic,
which treats of reasoning — and as the art of rea.son-
ing lies in deducing propositions whose truth does not
OF LOGIC. !5r
immediately appear, from others more known— -It M^ijl
be proper, before we proceed any farther, to examine
a little the different degrees of evidence that accom-
pany our judg-ments ; that we may be the better able
to distinguish in what cases we ought to have recourse
to reasoning, and what those propositions are, upon
■svhich, as a sure and unerring foundation, we may
ve..tuie to build the truth of others.
Sec. H. — Pro/iQsitions divided into Self-evident and
Demonstrable.
When any proposition is offered to the view of the
mind, if the terms, in which it is expressed, are un-
derstood ; upon comparing the ideas together, the
agreement or disagreement asserted is either imme-
diately perceived, or found to lie beyond the present
reach of the understanding. In the first case, the
proposition is said to be self-evident, and admits not of
any proof ; because a bare attention to the ideas them-
selves produces full conviction and certainty ; nor is
it possible to call in any thing more evident by way
of confirmation. But where the connexion or repug-
nance^ comes not so readily under the inspection of
the mind, there we must have recourse to reasoning ;
and if, by a clear series of proofs, we can make out
the truth proposed, insomuch that self-evidence shall
accompany every step of the procedure, we are then
able to demonstRate what we assert ; and the propo-
sition itself is said to be demonstrable. When we af-
firm, for instance, that it is impossible for the same thing
to be and not to be ; Vvdioever understands the terms
made use of, perceives, at first glance, the truth of
what is asserted ; nor can he, by any efforts, bring
himself to believe the contrary. The proposition
therefore is self-evident, and such that it is impossible
by reasoning to make it plainer ; because there is no
S
13S DUNCAN'S ELEMTENS
truth more obvious, or better known, from Avhich, as
a consequence, it may, be deduced. But if^ we sav,
this Tjorld had a beginning ; the assertion is indeed
equally true, but shines not forth with the same de-
gree of evidence . We iind great difficulty in conceiv-
ing how the world could be made out of nothing ; and
are not brought to a free and full consent, until by
reasoning v/e arrive at a clear view of the absurdity
involved in the contrary supposition. Hence this
proposition is of the kind v/e call demonstrable^ inas-
much as its truth is not immediately perceived by the
mind, but yet may be made appear by means of oth-
ers more known and obvious, whence it follows as an
unavoidable consequence.
Sec. III.-— rr7;t/ the second operation of the Mind is
coiijintd ivholhj to Intuition.
From what has been said, it appears that reason-
ing- is employed only about demonstrable proposi-
tiolis, and that our intuitive and self-evident percep-
tions are the ultimate foundation on which it rests.
And now we see clearly the reason, Avhy in the dis-
tinction of the powers of the understanding, as ex-
plained in the introduction to the treatise, the secorid
opei-ation of the m-ind was confined wholly to intui-
tive acts. Our first step, in the way to knowledge,
is to fui-nish ourselves with ideas. When these are
obtained, we next set ourselves to compare them to-
gether, in order to judge of their agreement or disa-
greement. If the relations we are in^ quest of, lie
immediately open to the view of the mind, the judg-
ments expressing them are self-evident ; and the act
of the mind, forming these judgments, is what we
call intuition. But if, upon comparing our ideas to-
gether, we cannot readily and at once trace their re-
lation, it then becomes necessary to employ search
OF LOGIC. u9
and examination, and call in the assistance of self-ev-
ident truths, which is what we properlv term rcasc?:-
ing. Every judgment, therefore, that is not intuitive,
being gained by an exercise of the reasoning faculty,
, necessarily belongs to the third operation of the mind,
and ought to be referred to it in a just division of the
powers of the understanding. Aiid indeed it is with
this view chiefly, that we have distinguished propo-
sitions into self-evident arnd demcnstrabie. Undef
ti:e first head are comprehended ail our intuitive jud?-
meiits, that is, all belonging to the second operation
of the mind. Demonstrable propositions are the
proper province of the reasoning faculty, and consti-
tute by far the most considerable p:.rt of. human
knov/ledge. Indeed reason extends also to matters
of experience and testimony, where the proofs ad-
duced are not of the kind called demonstraticn. But
i am here only considering the powers of the mind
as employed in tracing the relations between its own
ideas, in which view of things, every true proposition
is demonstrable ; tliough very often we iind ourselves
incapable of discovering and applying those interme-
diate ideas upon which the demonstration depends.
Sec. IV Selj-c-oident Truths ths f.rst Prind/des of
Reasoning.
Dem.onstrable propositions, therefore, belonging
properly to the third operation of the mind, I shall,
iur the present, dismiss them, and return to the con-
sideration of self-evident truths. These, as I have al-
ready observed, furnish the first principles of reason-
ing ; and it is certain, that if in our researches, v^^e
employ only such principles as have this character
of self-evidence, and apply them according to the
rules to be afterwards explained, v^-e shall be in no
danger of error, in advancing from one discovery to
140 DUNCAN'S ELEMENTS
another. For this I may appeal to the Avritings of
the mathematicians, which, being conducted by the
express model here mentioned, are an incontestible
proof of the firmness and stability of human kno^vl-
edge, when built upon so sure a foundation. For
not only have the propositions of this science stood ^
the test of ages, but are found attended with such in-
vincible evidence, as forces the assent of all vrho duly
consider the proofs upon which they are established.
Since then mathematicians are universally allowed
to have hit upon the right method of arriving at
truths—since they have been the happiest in the
choice, as well as application of their principles— it
may not be amiss to explain here the divisions they
have given of self-evident propositiciis ; that, by tread-
inp- in their steps, we m^ay learn something of that
justness and solidity of reasoning, for which they are
so deservedly esteemed.
Sec. Y.-^D^niUonsa great help to Clearness and Ev-
idence in Kjaowledg^.
First, then it is to be observed, that they have been
very careful in ascertaining their ideas, and hxmg
the signiiications of their terms. For this purpose
they begin with defrnitions, in v/hich the meaning oi
their v/ords 'is so distinctly explained, that they can-
rot fail to excite in the mind of an attentive reader
tl.e very same ideas as are annexed to them by the
writer. And indeed I am apt to think, that the clear-
ness avid irresistible evidence of matnemslicsii kncv.'I-
cdf^e, is oAving to nothing so much as tiiis care in
laying the foundation. Where the relation between
any two ideas is accurately and justly traced, it wiil
not be diliicult for another to com.prehend that rela-
tion, if in settiiig himself to discover it, he brmgs the
YtxY same ideas into corapaiison* But if, on tnc
OF LOGIC. Ul
contrary, he aHixes to his words ideas different from
those that were in the mind of him who first advanc-
ed the demonstration ; it is evident, that as the same
ideas are not compared, the same relation connot sub-
sist, insomuch that a proposition will be rejected as
false, which, had the terms been rightly understood,
must have appeared unexceptionably true. A squre,
for instance, is a figure bounded by four equal right
lines, joined together at right angles. Here the na-
ture of the angles m.ake no less a part of the idea,
than the equality of the sides ; and many properties
demonstrated of the square, Row fiom its being a rec-
tangular figure. If, therefore, we suppose a man
who has formed a partial notion of a square, compre-
hending only the qviality of its sides, without regard
to the angles, reading some demonstration that im-
plies also this latter consideration ; it is plain he
v/ouid reject it as not universally true, inasmuch as
it could not be applied w^here^the sides were joined
together at unequal angles, iror this last figure, an-
sv/ering still to his idea of a square, would be yet
found v."ithout the pixperty assigned to it in the^pro-
position. But if he comes Jiftervv-ards to correct his
iiollon, and render his idea complete, he will then
reachly own the truth and justness of the demon-
stiMtion.
Sec. VI. — Matheynaticians by beginning ivith thern.firo-
cure a ready recsption to the truths they advance,
Vre see, therefore, that nothing contributes so
much to the improvement and certainty of human
knowledge, as the having determinate ideas, and
keeping them steady and invariable in all our dis-
ccurses and reasonings about them. And on this
account it is, that mathematicians, as was beiore ob-
served, always begin by defining their terms, and
142 DUNCAN'S ELEIV'ENTS
distinctly unfolding the notions they are intended to-
express. Hence such as apply themselves to these
studies, having exactly the same vievrs of things, and
bringing always the very same ideas into compari-
son, readily discern the relations betv/een them, when
clearly and distinctly represented. Nor is tliere any
more natural and obvious reason for the universal re-
ception given to mathematical truths, and for that
harmony a,nd correspondence of sentiments vrhich
makes the distinguishing character of the literati of
this class.
Sec. Yll.-^The establiGhing cf Principles the Secoy.d
Stefi in Mathematical Kvoivled^e.
When they have taken this first step, and made
knov/n the ideas, whose relations they intend to in-
vestigate, their next care is, to lay down some self-
evident truths, which may serve as a foundation for
their future reasonings. And here, indeed, they pro-
ceed VAth remarkable circumspection, admitting no
principles but what fiow immediately from their de-
finitions, and necessarily force themselves upon a
mind in any degree attentive to its perceptions. Thus
a circle h. a figure formed by a right line, m.oving
round soii>e-%.£.d.pc^nt in the same plane. The fix-
ed point, round whTch the line is supposed to move,
and where one of its extrejnities terminates, is called
the centre of the circle. The other extremity, which
is conceived to be carried round, until it returns to
the point whence it first set out, describes a curve
running into itself, and termxed the circumference. All
right lines, drawn from the centre to the circumfer-
ence, are called radii. From these definitions com-
pared, geometricians derive this self-evident truth,
that tlie radii of the same circle are all equal one to cm-
other. I call it self-evident, because nothing more is
OF LOGIC. .143
required, to lay it open to the immediate preceptioa
-of the mind, than an attention to the ideas compar-
ed. For froiii the very nature of a circle it is plain,
that the circumference is every where distant from
the centre, by the exact length of the describing line .;
and that the several radii are in truth nothing more,
than one and the same line variously posited within
the figure. This short description will, I hcpe, serve
to give some little insight into the manner of deduc-
ing mathematical principles, as well as into the na-
ture of that evidence which accompanies them.
Sec. VIII. — Profiosi:io?:s divided into S^ieculative and
Practical.
And now I proceed to observe, that in all proposi-
tions we either affirm or deny some property of the
idea that constitutes the subject of cur judgment, or
we maintain that something may be done or effect-
ed. The first sort is called sjieculaiive propositions,
.as in the example mentioned above, the radii of the
&ame circle are all equal one to anothtr. The others
are called practicaU for a reason too obvious to be
mentioned ; thus, that a right line may be draix^n froTYi
one fioint to another^ is a practical proposition ; inas-
much as it expresses that something may be done.
Sec. IX. — Hence Mathematical Princijiles distinguish-
ed into Axioms and Postulates.
From this twofold consideration of propositions,
arises the twofold division of mathematical principles,
into cLxioms and iiostulates. By a.n axiov.i they under-
stand any self-evident speculative truth : as, that the
whole is greater than its parts : ihat,^hings equal to
one and the same things are equal to one another. But
a self-evident practical proposition is what they call
a postulate. Such are .these of Ruclid ; that a Jinite
144 DUNCAN'S ELEMENl^
right line may be continued directly forwards : that n
circle, may be described about any centre ivith any dis-
stance. And here we are to observe, that as in an
axiom^ the agreement or drsagTceiricnt betvv^een the
subject and predicate, must come under the imme-
diate inspection of the m.ind ; so in a fiostulate^ not
only the possibility of the thing asserted must be ev-
ident at first view, but also the nianner in vrhich it
may be effected. But where this manner is not of
itself apparent, the proposition comes auider the no-
tion of the demonstra,bIe kind, and is treated as such
by the geomatrical writers. Thus, to draw a line
from one point to another^ is assumed by Euclid as a
postulate^ because the manner of doing it is so obvi-
ous, as to require no previous teaching. But then it
is not equally evident, how we are to construct an
equilateral triangle. For this reason^ he advances it
as a demonstrable proposition, lays "itlown rules f(^r
the exact performance, and at the same time proves,
that if these rules are followed, the figure will be
justly described.
Sec. X. dnd demonstrable Profwsitions into Theorems
and Prgblcms.
This naturally leads me to take notice, Xh^iii's, self-
evident truths^ are distinguished into ditferent kinds,
according as they are speculative or practical ; so is
it also with c/(?/«0725-?m(^/r propositions. A dem.onstra-
ble speculative proposition is by mathematicians call-
ed a theorem. Such is the fiunous 47th proposition
of the first book of the Elements^ known by the name
of the Pithagoric theorem, from its supposed inventor,
Pithagoras^ xriz. That in every right-angled triangle ^
the square described upon the side subtending the right
angle, is equal to both the squares described upon the
containing the right angle. On the other hand,
OF LOGIC. 145
a demonstrable practical proposition is called a prob-
lem ; as where Euclid teaches us to describe a sgztarc
ufion a given right line.
Sec. XL — Corollaries are' obyjious deductions from The
orems or Probienis.
Since I am upon this subject, it may not be amiss
to add, that besides the four kinds of propositions al-
ready mentioned, mathematicians have also a fifth,
known by the name of corollaries. These are ucualiV
subjoined to theorems ov ^.robkms^ and difTer from theni
only in this, that they flow from what is there demon-
strated, in so obvious a manner as to discover their
dependence upon the proposition whence they are de-
duced, almost as soon as proposed. Thus Euclid hav-
ing demonstrated, that in every right-lined triangle^ all
the three angles taken together^ are equal to txvo right
angles; adds, by way of corollary, that all the three
angles of any one triangle take7i together, are equal to
all the three angles of any other triangle, taken together :
v.liich is evident at first sight ; because in all cases
they are equal to two right ones, and things equal to
two and tiie sam.e thing, are equal to one another.
Sec. XIL — Sc/wlia serves the fnirjioses of Annotations
or a Comment.
The last thing I shall take notice of, in the prac-
tice of the mathematicians, is vvhat they call their
scholia. They ?C£Q indifierently annexed to definitions,
propositions, or corollaries ; and ansvfer the sam.e pur-
poses as annotaiiciis upon a classic author. For in
them occasion is taken, to explain v.diatever may ap-
pear intricate and obscure in a train of reasoning ; to
ansv.er objections ; to teach the application and uses
of propositions ; to lay open the original and history
of the several discoveries made in the science ; and in
T
1 46 DUNCAN'S ELEMENTS
a word, to acquaint us with ail such particulars as de-
serve to be known, v/hether considered as points of
curiosity or profit.
Sec. XIII. — This Method of the Mathematicians imivei''
saly and a sure guide to Certainty.
Thus we have taken a short view of the so much
celebrated method of the m?Lthematicians ; which, to
any one Avho considers it witli a proper attention, must
needs appear universal, and equally applicable in other
sciences. They begin with definitions. From these
they deduce their axioms and postulates, which serve
as principles of reasoning ; and having thus laid a
firm foundation, advance to theorem.s and problems,
establishing all by the strictest rules of demonstration.
The corollaries flow naturally and of themselves.
And if any particulars are still v/anting to illustrate a
subject, or complete the reader's information ; these,
that the series of reasoning mpiV not be interrupted or
broken, are generally throv/n into scholia. In a sys-
tem of knovviedge so uniform and well connected, no
v> onder if we meet v/ith certainty ; and if those clouds
and da.rknesses, that deface other parts of human sci-
ence, and bring discredit even upon reason itself, are
here scattered and disappear.
Sec. XIV. — Self-evident Truths kn'jvm by the apjiarent
unavoidable Connexion betxVie7i the Subject and Pre-
dicate.
But I shall for the present wave these reflections,
which every reader of undei stem ding is able to make
of himself, and return to the considercition of self-evi-
dent propositions. It will, doubtless, be expected, af-
ter vv-hat has been here said of them, that I should
establish some criteria^ or m.arks, b}' v/hich they may
be distinguished. But I frankly own my inability in
OF LOGIC. \47
this respect, as not being able to conceive any thini^'
in tiieni more obvious and striking, than that self-evi-
dence which constitutes their very nature. All I have
therefore to observe on this head, is, that we ought to
make it our first carc, to obtain clear and determinate
ideas. When afterwards we come to compare these
together, if we perceive betv'eenany of them a neces-
sary and unavoidable connexion, insomuch that il is
impossible to conceive them existing asunder, with-
out destroying the very ideas compared ; we may then
conclude, that the proposition expressing this relation
is a principle, and of the kind we call. self-evident. In
the example m.entioned above,?//^ radii oftJie same circle
are all equal keHve en f.'^f;^?;5'^/T'fs, this intuitive evidence
shines forth in the clearest manner ; it being impossi-
ble for any one, who attends his own ideas, not to
perceive the equality here assei'ted. Fv'>r as the cir-
cumference is every where distant from ix\ft centre
by the exact length of the describing line ; the radii
drawn from the centre of the circumference, being
severally equal to this one line, must needs also be
equal among themselves. If vve suppose the radii
unequal, we at the same time suppose the circum-
ference m.ore distant from the centre in scm.e places
than in others ; from v/hich supposition, as it would
exhibit a figure quite different from a circle, we see
tliere is no separating the predicate from the subject
in the proposition, vrithout destroying the idea in re-
lation to which the com.parison was miade. The sam.e
thing vrill be found to hold in all our ether intuitive
perceptions, insomuch that v/e may establish this
as an universal criiencm^ whereby to judge of, and
distinguish them. I vv"ould not, however, be under-
stood to m.ean, as if this ready viev/ of the unavoida-
ble connexion between some ideas was any thing
really diiierent from self-evidence. It is, indeed.
U8 DUNCAN'S ELEMENTS
nothing more than the notion of self-evidence a little
\irifolded, and as it were laid open to the inspection of
the mind. Intuitive judgments need no other dis-
tinguishing marks, than that brightness which sur-
rounds them ; in lil^e manner as light discovers itself
hy its own presence, and the splendor it universally
diffuses. Bui I have said enougli of self-evident pro-
positions, and shall therefore now proceed to those of
lh<t demonstrable l^ind ; which, being gained in conse-
quence of reasoning, naturally leads us to the third
part of logic, where this operation of the understand-
ing is explained.
BOOK III.
OF REASONING.
CHAP. I.
«F EEJSCNII^JG IN GTL>:ERAL, AKD THE PARTS OF
V.'IIICH IT CONSISTS.
Sec. I. — Remote Relations discovered by mecms of in-
termediate Ideas.
\'\ E have seen hov7 the mind proceeds in furnish-
ing itself with ideas, and framing intuitive percep-
tions. Let us next inquire into the manner^ of dis-
covering those more remote relations, v/hich, lying
i\i a distance frbm the understanding, are not to be
traced but by means of a higher exercise of its povr-
e;rs. It often happens in comparing ideas together,
that their agreement or disagreement cannot be dis-
cerned at first viev/p especially if they are of such a
OF LOGIC. 149
nature, as not to admit of an exact application one to
another. When, for instance, v/e compare t^vo fig-
ures of a different make, in order to judge of their
equality or inequality, it is plain, that by barely con-
sidering the figures themselves, Ave cannot arrive al
an exact determination ; because, by reason of their
disagreeing form.s, it is impossible so to put them to-
gether, as that their several parts shall mutually co-
incide. Here then it becomes necessary to look out
for some third idea, that v.'ill admit of such an appli-
cation as the present case requires ; wherein it vre
succeed, all diiticulties vanish, and the relation vre are
in quest of may he traced with ease. Thus right-
lined figures are all reducible to squares, by means
CI v/hich we can measure their areas, and determine
exactly their agreement or disagreement in point of
niagmtuce.
Sec. II. — This manner of arriving at Truth a^.d Urm-
ed Reaso7ii?2g.
If now it be asked, how any tliird idea can serve to
discover a reIa:ion betv/een two others ; I answer, by
being compared severrdly with these others ; for such
a comparison enables us to see how far the ideas, with
wliich this third is compared, ai^e corinected or dis-
joined between themselves. In the example men-
tioned above, c=^f two right-lined fi.gures, if we compare
each cf them vrith some square whose area is known,
raid find the one exactly equal to it, and the other less
by a square-inch greater than that of the second.
This manner of determining the relation between any
two ideas, by the invention of some third with which
they may be compared, is that v/hich we call reason-
ing, and indeed the chief instrument, by which vre
push on cur discoveries, and enlarge our knowledge.
■The great art lies, in finding out such intennedi&te
150 DUNCAN'S ELEMENTS
ideas, as, when compared Avith the others in the ques-
tion, will furnish evident and known truths ; because,
as will afterwards appear, it is only by means of them,
that we arrive at the knowledge of what is hidden and
remote.
Sec. III. — Tke parts that constitute an Act of Reason-
ing and a Syilogum.
From Vv'hat has been said, it appears that every act
©f reasoning necessarily includes three distinct judg-
ments ; two, wherein the ideas, v/hose relation we
"want to discover, are severally compared with the
middle idea ; and a third, wherein they are themselves
connected or disjoined according to the result of that
comparison. Now as in the second part of logic, our
judgments when put into words, were called propo-
sitions— so here, in the third part, the expressions of
our ■'"easonings are termed syllogisms. And hence it
follows, that as every act of reasoning implies three
several judgments, so every syllogism must include
three distinct propositions. When a reasoning is thus
put into v.crds, and appears in form of a syllogism,
the intermediate idea, made use of to discover the
agreement or disagreement we search for, is called
the mzddtt term ; and the two ideas them.selves, with
which this third is compared, go by the name of the
extremes.
Sec. IV. — luijtancc^ Man and Accountahleness.
But as these things are best illustrated by exam-
ples ; let us, for instance, set ourselves to enquire,
vjhether men are ^accountable for thdr actions. As the-
relation between the ideas of man and accountahleness
comes not vfithinthe immediate view of the mind, our
first care must be, to find out some third idea, that
will enoble us the mere easily to discover and trace it»
OF LOGIC. 151
A very small measure of reflection Is siifficier.t to in-
form us, that no creature can be accountable for his
actions, unless w.-e suppose • im capable ot flistinguish-
iny; the good from the bad ; that is. unless we suppose
him possessed of reason. Nor is this alone sufficient.
For what would it avail him, to know good from bad
actions, if he had no freedom of cnoice, nor could avoid
the one, and pursue the other ? Kence it becomes
necessary to take in both considerations in the present
case. It is at the same time equally apparent, that,
v>-her2ver there is this ability of distinguisiiing good
from bad actions, and pursuing the one and avoiding'
the other, there also a creature is accountable. Vv'e
have then got a third idea, with which acc<juntcMene8s^
is inseparably connected, viz. reason and liberty;
which z::q here to be Considered as making up one
complex conception. Let us now take this middle
idea, and compare it with the other term in the quesr
tion, viz. nicn^ and vre all know by experience, that %
may be amrmed of him. Having' thus, by means of
the intermediate idea, formed two several judgmentfey
viz. that man is possessed cf reason and liberty ; and
tkat reacon and liberty imply accoiintableness ; a third
obviously and necessarily follows, viz. that man is ac-
countable for his actions. Here then we have a com-
plete act of reasoning, in which, according to what has
been already observed, there are three distinct judg-
ments ; two that may be styled previous, inasmuch as
they lead to the other, and arise from comparing the
middle idea with the tv/o idea^ in the Cjuestion ; the
third is a consequence cf these previous acts, and
flows from combining the extreme ideas between them-
selves. If now we put this reasoning into words, it
exhibits what logicians term a syllogism, and, when
proposed in due forni, runs thus :
Eveiy creature possesced cf reason aud liberty is accounts.-
ble for his actions.
152 DUNCAN'S ELEMENTS
Man is a creature possessed of reason and liberty.
Therefore man is accountable for his actions.
Sec. v.- — Premises.) conclusion^ extremes, middle term.
In this syllogism vv'e may observe, that there are
three several propositions, expressing the three judg-
ments implied in the act of reasoning, and so dispos-
ed as to represent distinctly what passes within the
mind, in tracing the more distant reiatioDs of its ideas.
The two first propositions answer the two previous
judgments in reasoning, and are called the fif^emisesy
because they are placed before the other. The third
is termed the conclusion, as being ga,ined in conse-
quence of what was asserted in the premises. We
are also to remember, that the terms expressing the
tvro ideas whose relation we enquire after, as here
i;ian and accountabkness, are in genera), called the ex-
tremes ; and that the intermediate idea, by means of
which the relation is traced, viz. a creature f2os^essed
of reason and liberty, takes the name of the middle term.
Hence it follows, that by the ^ir^mises of a syllogism,
we are always to understand the two propositions,
wdiere the middle term is severally compared with
extremes ; for these constitute the previous judgments,
whence the truth we are in quest of is by reasoning
deduced. The conclusion is, that otlier propositions,
in which the extremes themselves are joined or sepa-
rated, agreeably to what appears upon the above com-
parison. All this is evidently seen in the foregoing
syllogism, where the two first propositions, which
represent the premises, and the third, v.hich makes
the conclusion, are exactly agreeable to the denni-
tifjns here given'.
Sec. VI. — yMujor and Minor Term, ^fajor and Minor
Preposition.
Before we tal-ie leave of this article, it will be far-
ther necessary to observe, that as the conclusion is
OF LOGIC. 153
made up of the extreme terms of the syllcgism ; so
that extreme, which serves as the predicate of the
conclusion, goes by the name of the major term : the
other extreme, which makes the subject in the same
proposition, is called the fninor teivn. From this dis-
tinction of the extremes, arises also a distinction be-
tween the premises, wiiere these extremes are sevcr-
ailv compared with the middle term. That proposi-
tion, which compares the greater extreme, or t\\Q.
predicate of the conclusion, with the middle term, is
called the riiajcr firofiosition : the other, wherein the
same middle term is compared with the subject of
the conclusion, or lesser extreme, is called the mitior
jirctiodtion. Ail this is obvious from the syllogism
already given, where the conclusion x^^man is account-
able for his actions. Fof here the predicate, account-
able for his actions^ being connected v*^th the middle
tenii in the first of the two premises. Every creature
possessed cf reason and liberty is accouniahlefor his ac-
tio7i3^ gives what we call the 7najor jircpodtion. In
the second of the premises, man is a creature p.ossess-
ed cf reason and liberty y Ave find the lesser extreme,
or subject of the conclusion, viz. 77za?2, connected with
the same middle term, whence it is known to be the
TTiinor prcliosiiion. I shall only add, that when a syl-
logism is proposed in due form, the major proposition
is aivrays placed first, the minor next, and the con-
clusion last, according as we have done in that offered
above.
Sec. VII. — Judgmejitand Proposition^ Reasoning and
Syllog-ism di^sti7iguisk ed.
Having thus cleared the w^ay, by explaining such
terms, as we are likely to have occasion for in the
progress of this treatise ; it may not be amiss to ob-
serve, that though we have carefully distinguished
U
154 BUNCAlS^s ELEMENTS
between the act of reasonings and a syllogism^ v/hich
is no more than the expression of it, yet common
language is not so critical on this head ; the term
rm-so;?/;?.^ being promiscuously used, to signify either
the judgments of the mind, as they follow one anoth-
er in train, or the propositions expressing these judg-
ments. Nor need we wonder that it is so, inasmuch
as our ideas, and the terms appropriated to them,
are so connected by habit and use, that our thoughts
fall as it Avere spontaneously into language, as fast as
they arise in the mind ; so that even in our reasonings
within ourselves, we are not able wholly to lay aside
words. But notwithstanding this strict connexion be-
tween mental ?iXidi verbal reasoning, if I may be allow-
ed that expression, I thought it needful here to dis-
tinguish them, in order to give a just idea of the m.an-
ner^ of deducing one truth from another. While the
mind keeps the ideas of things in view, and combines
its judgments according to the real evidence attend-
ing the^n, there is no great danger of mistake in our
reasonings ; because v/e carry our conclusions no
farther than the clearness of our perceptions warrants
lis. But where w^e make use of words, the case is
often otherv/ise ; nothing being more common, than
to let them pass without attending to the ideas they
represent ; insomuch that we frequently com.bine ex-
pressions, v/hich upon examination appear to have no
determinate meaning. Kence it greatly imports us
to distinguish between reasoning and syllogism ; and
to take care, that the one be in all cases the true and
just representation of the other. However, as I am
unwilliiV to recede too far from the common forms
of speech, or to multiply distinctions without neces-
sity, I shall hence forward consider propositions as
representing the real judgments of the mind, and syl-
logisms as the true copies of our reasonings ; which
OF LOGIC. 155
indeed they ought always to be, and undoubtedly al-
ways will be, to men v/ho think justly, and are desir-
ous of arriving at truth. Upon this supposition there
will be no danger in using the words judgnient and
proposition promiscuously ; or in considering reason-
ing as either a combination of various judgments, or
of the propositions expressing them ; because, being
the exact copies one of another, the result will be in
all cases the same. Nor is it a small advantage, tliat
we can thus conform to common speech, without con-
founding our ideas, or running into ambiguity. By «
this means we bring ourselves upon a level with other
men, readily apprehend the meaning of their expres-
sions, and can with ease convey our own notions and
sentiments into their minds.
Sec. VIII. — dn a single Act of Rea.^oinng. the Premis- •
€8 must be intuitive Trut/zs.
These tilings premised, vre may in the general
define reasoning to be aii act or cfieration of the mindy
declucijjg some unkno'ion ^iro^iositioyi^from other firevioiis
ones that are evideiit and kno'ivn. These previous
propositions, in a simple act of reasoning, are only
two in number ; and it is always required that they
be of themselves apparent to the understanding, inso-
much that Ave assent to and perceive the truth of
them as soon as proposed. In the syllogism given
above, the premises are supposed to be self-evident
truths, otherwise the conclusion could not be inferred
by a single act of reasoning. If, for instance, in the
major, every creature possessed .of reason and liberty is
accountable for his actions, the connexion between the
subject and predicate could not be perceived by a bare
attention to the ideas themselves ; it is evident, that
this proposition vrould no less require a proof, than
the conclusion deduced from it. In this case, a new
]56 DUNCAN'S ELEMENTS
ir.iddle term must be sought for, to trace the conrjex-
ion here supposed ; and this of course furnishes an-
other syllogism, by Avhich having established the
proposition in question, we are then, and not before,
at liberty to use it in any succeeding train of reason-
ing. And should it so happen, that in this second
essay, there was still some previous proposition whose
truth did not appear at nrst sight ; vre must then have
recourse to a third syllogism, in order to lay open
that truth to the mind ; because so long as the premis-
es remain uncertain, the conclusion built upon them
must be so too. When by conducting our thoughts
in this manner, v/e at last arrive at some syllogism,
where the previous propositions are intuitive trutns ;
the mind then rests in full security, as perceiving
that the several conclusions it has passed through,
stand upon the immoveable foundation of self-evi-
dence, vjrA) V, hen traced to their source, terminate
in it.
Sec. IX. — Rcaf.Gni7'ig^ in the highest Kxercise of it-j on-
ly a Concatenation of Syllogisms.
Vv^e see, therefore, tiiat in order to infer a conclu-
sion by a single act of rea.soning, the premises must
be intuitive propositions. Where they are not, pre-
vious syllogisms are required, in which case reason-
ing becomes a com.plicated act, taking in a variety of
successive steps. This frequently happens in trac-
ing the more remote relations of our ideas, where
many middle terms being called in, the conclusion
cannot be made out, but in consequence of a series of
syllogisms follovving one another in train. But al-
though in this concatenation of propositions, those
that form the premises of the last syllogism, are of-
ten considerably removed from self-evidence ; yet if
^'c trace the reasoning backwards, we shall find them
OF LOGIC. I5r
the conclusions of previous syllogisms, whose premis-
es approach nearer and nearer to intuition, in prc-
porticn as wt advance, and are found at last to ter-
P_iinate in it. And if after having thus unravelled a
demonstration., vre take it the contrary way, ?j\d ob-
serve how the mind, setting ouf ^vith intuitive per-
ceptions, couples them together to form a conclusion
' — how, by introducing this conclusion into another
syllogism, it still advances, one step farther; and so
proceeds, making every new discovery subservient
to its future progress — we shall then perceive clearly,
that reasoning, in the highest exercise of that facul-
ty, is no more than an orderly combination of those
simple acts, v/hich we have already so fully explain-
ed. The great art lies, in so adjusting our syllogisms
one to another, that the propositions severally made
use of, as premises, may be manifest consequences
of what goes before. For as by this means, every
conclusion is deduced from kno^^m and established
truths, the very last in the series, how far soever v.-e
carry it, v/ill have no less certainty attending it, than
the original intuitive perceptions themselves, in which
the vrhole chain of syllogisms takes its rise.
Sec. X. — Requires intuitive Ccvtainty in every Stefi of
the Progression.
■ Thus v,-e see, that reasoning, beginning with first
principles, rises gradually from one judgment to an-
other, and connects them in such manner, that every
stage of the progression brings intuitive certainty
along with it. And now at length we may clearly
understand the definition given above, of this distin-
guishing faculty of the human mind. Reason, we
have said, is the ability of deducing unknown truths,
from prmciples or propositions that are already known.
This evidently appears, by tiie foregoing account^
158 DUNCAN'S ELErvIENTS
where we see, that no proposition is admitted into a
syllogism, to serve as one of the previous judgments
on which the conclusion rests, unless it is itself a
known and established truth, v.hose connexion with
self-evident principles has been already traced.
Sec. XL — Self-evident Truths^ the ultimate Foundation
of all Science and Certainty.
There is yet another observation which naturally
offers itself, in consequence of the above detail, viz,
that all the knowledge acquired by reasoning, how far
soever we carry our discoveries, is still built upon our
intuitive perceptions. T-cwards the end of the last
part, we divided propositions into self-evident and de-
monstrable, and represented those of the self-evident
kind, as the foundation on which the whole super-
structure of human science rested. This doctrine is
now abundantly confirmed by what has been deliver-
ed in the present ciiapter. We ha.ve found, that eve-
ry discovery of human reason, is the consequence of
a train of syllogisms, which, when traced to their
source, always terminate in self-evident perceptions.
When the mind ai^ri'v'es at these primitive truths, it
pursues not its enquiries fartlier, as well knowing, that
no evidence can exceed that which flows from an im-
mediate view of the agreement or disagreement be-
tween its ideas. And hence it is, that in unravelling
any part of knowledge, in order to come at the foun-
dation on which it stands ; intuitive truths are always
the last resort of the understanding, beyond which it
aims not to advance, but possesses its notions in per-
fect security, as having now reached the very spring
and fountain of all science and certainty.
OF LOGIC. 159
CHAP. II.
OF THE SEVERAL KINDS OF REASONTICG, AND FIRST
OF THAT BYWKTCH:.WE DETERMINE THE GENERA
AND SPECIES OF THINGS.
w=
Sec. I. — Reasoning Twofold.
E have endeavoured, in the foregoing chapter,
to give as distinct a notion as possible, of reasoning,
and of the manner in v.hich it is conducted. Let us
now enquire a little into the discoveries made by this
faculty, and what those ends are, which we have prin-
cipally in view in the exercise of it. All the aims of
human reason may, in the general, be reduced to these
two : 1 . To rank things under those universal ideas
to which they truly belong ; and 2. To ascribe to
them their several attributes and properties, in conse-
quence of that distribuuon.
Sec. II. — The Jirst kind regards the Genera and S/ic-
cies of Things.
First, then I say, that one great aim of human rea-
son is, to determine the genera and species of things'
We have seen, in the first part of this treatise, how
the mind proceeds in fi'aming general ideas. We
have also seen, in the second part, how, by means of
these general ideas, we come by universal propositions.
Now as in these universal propositions, we affirm
some property of a genus or species, it is plain, that
we cannot apply this property to particular objects,
till we have first determined, v/hether they are com-
prehended under that general idea, of which the prop-
erty is affirmed. Thus there are certain properties
belonging to all e~osn numbers, which nevertheless
cannot be applied to any particular number, until we
360 DUNCAN'S ELEMENTS
liave first discovered it to be of the species expressed
by that general name. Hence reasoning- begins with
referring things to their several divisions and classes
ill the scale of our ideas ; and as these divisions are
all distinguished by peculiar names, we hereby leani
to apply the terms expressing general conceptions,
to such particular objects, as come under our imme-
dia.te observation.
Sec. Ill-- — The Steps hy 'vjkich nve arrivs at Conclu-
sions of this sort.
Now in order to arrive at these conclusions, by
which the several objects of perceptions are brought
under general names, tv/o thing:s are manifestly ne-
cessary. First, that vre take a view of the idea itself
denoted by that general name, and Cvirefuliy attend
to the distinguishing marks which serve to character-
ize it. Secondly, that we compare this idea v/ith the
object under consideration, observing diligently where-
in they agree or diiier. If the idea is found to cor-
respond with the particular object, we then, without
hesitation, apply the general name ; but if no such
correspondence intervenes, the conclusion must ne-
cessarily take a contrary turn. Let us, for instance,
take the number eight., and consider by what steps
we are led to pronounce it an even number. First
then we call to mind the idea signined by the expres-
sion, an even number^ viz. that it is a number divisible
into tivo equal parts. We then compare this idea .
with the number eighty and finding them maniil^stly
to agree, see at once the necessity of admitting the
conclusion. These several judgments therefore,
transferred into language, and reduced to the form of
a syllogism, appear thus :
Evei-y number that may be divided into two equal parts.
is an even number.
f
OF LOGIC. 16 1
The nUTTiber eight may be divided into nvo equal parts.
Therefc'ie the number eight, is an eve?i number.
Sec. Vs.— 'Those i,tep^ ahvays follov:ed, though in fa-
uiiliLr cases %ve do not aiivays attaid to them.
I have made choice of this example, not so much for
the sake ©f the conclusion, which is obvious enough
and might have been obtained without all that parade
of words ; but chiefly because it is of easy compre-
hension, and serves "at the same time distinctly to
exhibit the form of reasoning by which the undei-
standing conducts itself in all instances of this kind.
And here it maybe observed, that where the general
idea, to which particular objects are referred, is very
familiar to the mind, and frequently in viev/ ; this-
reference, and the application of the general name,
seem to be made withcnt any apparatus of reasoning.
When vre see a horse in the fields, or a dog in the
street, we readily apply the name of the species ;
habit, and a fdmiliar acquaintance with th^ general
idea, suggesting it instantaneously to the mind. \'/e
are not, hov.xver, to imagine on this account, that the
understanding departs from the usual rales of just
thinking. A fi'equent repetition of acts begets a hab-
it ; and habits are attended with a certain prompt-
ness of execution, that prevents cur observing tii©
several steps and gradations, by which any course of
action is accom.plished. But in ether instances, where
we iudge not by precontracted habits, as when the
v^eneral idea is very complex, or less famniiar to the
mind ; we always proceed according to the form of
reasoning established above. A goldsmith, for m-
stance, who is in doubt as to any piece of metal,
whether it be of the species called gold, first exammes
its properties, and then comparing them w^ith the
general idea signified by that name, if he find a per-
W
I
162 DUNCAN'S ELEMENTS
feet correspoBdence, no longer hesitates under what
class of metals to rank it. Now what is this, but
following step by step those rules of reasoning, which
we have before laid down as the standards, by which
to regulate our thoughts in all conclusions of this
kind V
Sec. V. — The Great Importance of this Branch of
Reasoning ;
Nor let it be iniagined, that our researches here, be-
cause in appearance bounded to the imposing of gen-
eral names upon particular objects, are therefore tri-
vial and of little consequence. Some of the most
considerable debates ?imong mankind, and such too,
as nearly regard their lives, interest, and happiness,
turn wholly upon this article. Is it not the chief em-
ployment of our several courts of judicature, to de-
termine, in particular instances, what is law, justice,
and equity ? Of v/hat importance is it, in many cas-
es, to decide aright, whether an action shall be term-
ed murder or manslaughter ? We see, that no less
than the lives and fortunes of men depend often upon
these decisions. The reason is plain. Actions, when
once referred to a general idea, drav/ siter them all
that mav be afhrmed of that idea ; insomuch that the
determining the species of actions, is all one with de-
termininp- vv^hat proportion of praise or dispraise,
commendation or blame, Sec. ought to follow them.
For as it is aliov/ed that murder deserves death, by
brin,2:ing any particular action under the head of mur-
der, Ve of course decide the punishment due to it.
Sec. Y\.—And the eract observance of it practised by
Ti lai hematic ians .
Psut the great importance of this branch of reason-
ing, and the necessity of care and circumspection, iu
OF LOGTC. 16-3
referring particular objects to general ideas, is still
farther evident from the practice of the mathemati-
cians. Every one who has read Euclid^ knows, that
he frequently requires us to draw lines through cer-
tain points, and according to such and such direc-
tions. The figures then ceresulting are often squares,
parallelograms, or rectangles. Yet Euclid never sup-
poses this from their bare appearance, but always de-
monstrates it upon the strictest principles of geome-
try. Nor is the method he takes, in any tiling dif-
ferent from that described above. Thus, for instance,
having defined a square to be a figure bounded by
four equal sides, joined together at right angles ;
when such a figure arises in any construction previ-
ous to the demonstration of a proposition, he yet nev-
er calls it by that name, until he has shown that the
sides are equal, and all its angles right ones. Now
tnis is apparently the same form of reasoning we
have before exhibited, in proving eight to be an even
number ; as will be evident to any one v/ho reduces-
it into a regular syllogism. I shall only add, that
when Euclid has thus determined the species of any
figure, he is then, and not before, at liberty to ascribe
to It all the properties already demonstrated of that
figure, and thereby render it subservient to the future
course of his reasoning.
Sec. VII. — Fixed and invanable Ideas^ vdth a steady
apjilication of Xamesyrenders this part of Knowledge
both &asy and certain.
Having thus sufficiently explained the rules by
which we are to conduct ourselves, in ranking par-
ticular objects under general ideas, and show their
conformity to the practice and manner of the mathe-
maticians ; it remains only to observe, that the true
way of rendering this part of knowledge both easy
164 DUNCAN'S ELEMENTS
and certain, is, by habituating ourselves to clear and
determinate ideas, and keeping tiiem steadily annex-
ed to their respective names, i^^or as all our aim is,
to annly general ^vord3 aright, if these words stand
ibr 'invariable ideas, that are perfectly known to tne
raind, andean be readily distinguished upon occasion,
tWf^i>e\viIl be little danger of mistake or error in our
rea.ionings. Let us suppose, that by examining^ any
Gh'cct, and carrying our attention successively from
-n- part to another, we have acquainted ourselves
w = :h the several particulars observable in it. if among
these we fmd such as constitute some general idea,
friimcd and settled beforehand by the understanding
and distinguished by a particular name ; the resem-
bllnce; thus known and perceived, necessarily deter-
mines tJie species of the object, and thereby gives it
a pp-ht to the name by which triat species is called.
-Thusriour equal sides, joined together at right an-
o-lPs, make up the notion of a square. As this is a
i^v-d and invariable idea, without which the genei-al
T^ame cannot be applied, we never call any particular
f n-v-/- a sqiior-, until it appears to have these several
^ w;-."l:ons ; and contrarily, wherever a figure is found
:,/,-V, th^se conditions, it necessarily takes the name
^^'^souare. The same will be found to hold m ail
oTf other reasonings of this kind ; where notiung can
^.,.,.^ o>.y diffcultv but the want of settled Kieas.—
Xrfov;n-tance, we'have not determined within our-
«"ives, the precise notion denoted by the word 7«a«-
lau^Iiter^ will be impossible for us to decide, wnet..-
era^v particular action ought to bear tuat name^
lv^c-"'=-, however nicely we examine the action itsea,
v^t b;in- strangers to the general idea with whicii it
is to bexompared, we are utterly unahle to judge of
their agreement or disagreement. But if we ta^e
• care to r^^vuove this obstacle, and distmctly trace tne
OF LOGIC. 165
tv.-o ideas under consideration, all difficulties vanish,
£indthe resolution becomes both easy and certain.
Sec. VIII.— ^y *"^- « Conchicty Certainty and Demon-
" stration might be introduced into other Parts cfKno'Wi-
edge as ivtll as Mathematics.
Thus we see cf what importance it is, towards the
improvement and certainty of human knowledge, that
^v'^ accustom ourselves to clear and determinate ideas,
and a steady amplication cf words. Nor is this so ea-
sy a task as some may, perhaps, be apt to imagine ;
•; ^,..,„;^;p,^ both a comprehensix e understanding, and
ijre^-rconniiand of attention, to settle the precise
bounds of our ideas, when they grow to be very com-
To'cx, and include a multitude ol particulars, isay,
end after these limits are duly fixed, there is a cer-
tain ciuickness of thought and extent of mind requir-
J?^ towards keeping the several parts in view, tliat m
com-oaririg our ideas one with another, none of them
may'be -oveLiooked. Yet ought not these difficulties
to discourage us ; though great, they are not unsiir-
mount^ble, and the advantages arising from success
will amplv recompence our toil. The certainty and
easv a-pniication of mathematical knowledge is whol-
ly owing to the exact observance of this mle. And
I am apt to imagine, that if we were to employ the
same care about all our other ideas, as mathemati-
cians have^ done about those of number and magni-
tude, by forming them into exact combinations, and
distiu£;uishing these combinations by particular names,
in oraer to keep them steady and invariable ; we
would soon have it in our power to introduce certain-
ty and demonstration into other parts of human
knovv ledge.
ISG DUNCAN'S ELEMENTS
CHAP. III.
OF REASONING AS IT REGARDS THE POWERS AXD
PROPERTIES OF THINGS, AND THE , RELATIOXS
OF OUR GENERAL IDEAS.
Sec. I. — The Distinction of Reasoning.'^ as it regards the
Sciences, and as it concerns common JUfo.
W E come now to the second great end which men
have in view hi their reasonings, namelv, the disrov-
ering and ascribing to things their several attributes
and properties. And here it will be necessary to
distmguish between reasoning, as it regards the scil
ences, and as it concerns common life. In the scien-
ces, our reason is employed chiefiv aJDOut universa-
triiths,it being by them alone that the bounds of hu-
man knowledge are enlarged. Hence the division of
things, into various classes, called otherv/ise genera
and species. For these universal ideas, being'set up
as the representatives of many particular things,
whatever is affirmed of them, may also be affirmed'^cf
all the individuals to v/hich they belong. Murder,
for instance, is a general idea, representing a certain
species of human actions. Reason tells us, that the
punishment due to it is death. Hence every narticu-
lar action coming under the notion of 7?iurde?^*h^s the
punishment of death allotted to it. Here then we ap-
ply the general truth to some obvious instance, and
this is what properly constitutes the reasoning of com-
mon life. For men in their ordinary transactions and
intercourse one with another, have for the most part
to do only with particular objects. Our friends and
relations, their characters and behaviours, the con-
stitution of the several bodies that surround us, and
the uses to v/hich they may be applied, are what
OF LOGIC. 167
chiefiy engage our attention. In all these we reason
about particular things ; and the \vhole result of our
reasoning is, the applying the general truths of the
sciences to the ordinary transactions of human life,
Vrhen we see a viper, we avoid it. Wherever v.^e
have occasion for the forcible action of water, to mo^•e
a body that niakes considerable resistan(^e, vre take
care to convey it in such a manner, that it shall fail
upon the object with impetuosity. Now all this hap-
pens, in consequence of our familiar and ready appli-
cation of these two general truths : the bite of a viper
is mortal: nv at er falling on a body ivithimfietuosity,^ acts
very forcibly to^vards setting it in motion. In hke man-
ner, if we set ourselves to consider any particular
character, in order to determine the share of praise or
dispraise that belongs to it, our great concern is, to
ascertain exactly the proportion of virtue and vice.— -
The reason is obvious. A just determination, in all
cases of this kind, depends entirely upon an applica-
tion of these niaxims of m.oraiity : virtuous actions
deserve jiraise : vicious actions deserve blame.
Sec. II. — The Steps by Kvhich ive proceed in the Reason-
ing of common Life.
Hence it appears, that reasoning, as it regards com-
mon life, is no more than the ascribing the general
properties of things to those several objecis with
which we are immediately concerned, according as
they are found to be of that particular division or class
to which the properties belong. The steps, then, by
which v^e proceed, are manifestly these : First, we
refer the object under consideration to some general
idea or class of things. We then recollect the sev-
eral attributes of that general idea ; and, lastly, as-
cribe all those attributes to the present object. Thus
hi considcrlngr the ciiaracter of Sempronlus.^ if we find
168 DUNXAN's ELEMENTS
it to be of the kind called virtuous ; Vv-ben we at tlic
same time reflect, that a -virtuous character is deserv-
ing of esteem, it naturally and obviously follows, that
8e:nfirordus is so too. These thoughts put into a %/-
iogisjn^ in order to exhibit the form of reasoning here
required, runs thus :
Every virtuous man is worthy of esteem.
Setnpromus is a virtu aus man :
Theretore Senipronius is worthy of esteem>
Sec. III. — The Connexion and Dcpcnder.cc of the two
grand Branches of Reasoning one up.on another.
Bv this syllogism it appears, that before we affirm
any thing of a particular object, that object must be
referred to some general idea. Seivfironius is prc-
r.ounced v/orthy of esteem, only in consequence of his
bein^^ a virtuous man, or coming under that i^eneral
notion. Hence v/e see the necessary connexion of.
the various parts of reasoning, and the dependence
thev have one upon another. The determining the
^eiiera and species of things is, as we have said, one
exercise of human reason ; and here v/e iind that this
exercise is the first in order, and previous to the oth-
er, Vv'hich consists in ascribing to them their pov/crs,
pronerties, and relations. But when v.'e have taken
this'nrevious step, and brought particular objects un-
der general names ; as the properties we ascribe to
them are no other than those of the general idea, it is
plain, that in order to a successful progress in this
part of knovr- ledge, we must thoroughly acquaint cur-
selves with the several relations and attributes of these
our general ideas. When this is done, the other part
vy-iil ije easy, and require scarce any labour of thought,
as being no more than an application of the general
form cf reasoning represented in the foregoing syllo-
crsm. Now, as vre have already suJiciently shown,
OF LOGIC. 169
"how we are to proceed in determining the genera aiid
species of things, which, as vv^e have said, is the pre-
vious step to this second branch of human knov, ledge ;
all llu.t 13 farther wanting to a due explanation of it
is, to ofrer some considerations, as to the manner of
investigating tiie general relations of cur ideas. This
is the highest exercise of the powers of the under-
standing, and that by means whereof, vre arrive at the
discovery of universal truths ; insom.uch that our de-
ductions in this way, constitute chat particular species
of reasoning which, we have before said, regards prin-
cipally the sciences.
Sec. IV. — Two things required to make a good P.cms-
cner.
But that we may conduct oitr thoughts with some
order and method, we sh"all begin with observing, that
the rela.icns of our general ideas are of tvro kinds.
Either s^ich as immediately discover themselves, upon
comparing the ideas one with another ; or such, as
being more remote and distant, require art and con-
trivance to bring them into view. The relations of
the first kind, furnish us with intuitive and self-evident
truths : those of the second are traced by reasoning,
and a due application of intermediate ideas. It is oi
this last kind that wx are to speak here, having dis-
patched what was necessary v\ith regard to the other
in the second part. As therefore, in tracing the more
distant relations of things, we must always have re-
course to intervening ideas, and are more or less suc-
cessful in our researches, according to cur acquain-
tance with these ideas, and abihty of applying them ;
it is evident, that to make a good reasoner, two things
are principally required. Firsts an extensive knowl-
edge of those intermediate ideas by means of which
things may be compared one with another. Second^
X
170 DUNCAN'S ELEMENTS
/t/, the skill and talent of applying them happily, in all
particular instances that come under consideration.
Sec. V. — First^ an exter^ive Knowledge of intermedi'
ate Ideas.
First, I say, that in order to our successful progress
in reasoning, v/e must have an extensive knov.iecige of
those intermediate ideas by means of which things
may be compared one vrith another. For as it is not
every idea that will ansvrer the purpose of our enqui-
lics, but such only as are peculiarly related to the ob-
jects about which We reason, so as by a comparison
■with them, to furnish evident and known truths ;
nothing is more apparent, than that the greater vari-
ety of conceptions we can call into view, the more
likely v/c are to find some among them that will help
us to the truths here required. And indeed it is found
to hold in experience, that in proportion as we enlarge
our viev/ of things, and grow acquainted with a mul-
titude of different objects, the reasoning quality gath-
ers strength. For by extending our sphere of knowl-
edge, the mind acquires a certain force and penetra-
tion, as being accustomed to examine the several ap-
pearances of its ideas, and observe what light they
cast one upon another.
Sec. VI. — To excel in any one Brarich of Learnings
Tje must in general be acquainted with the whole cir'
cle of Arts and Sciences.
And this I take to be the reason, that in order to
excel remarkably in any one branch of learning, it is
iiecessary to have at least a general acquaintance with
the vv'hole circle of arts and sciences. The truth of
it is, all the vrtrious divisions of human knovviedge are
very nearly related among themselves, and innurner-
iibie instances serve to illustrate and set off each oth-
OF LOGIC. 171
<er. And although it is not to be denied, that by an
obstinate application to one branch of study, a man
may make considerable progress, and acquire some
degree of emint:ice in it ; yet his views will be ahvays
narrow and contracted, and he v.ill want that masterly
discernment which not only enables us to pursue our
discoveries with ease, but also in laying them open to
others, to spread a ceitain bi-ightness around them.
I would not, hov/ever, here be understood to mean,
that a general knowledge alone is sufficient for ail the
purposes of reasoning. I only recommend it as prop-
er to give the mind a certain sagacity and quickness,
and qualify it for judging aright in the ordinary oc-
currences of life. But when our reasoning regards a
particular science, it is farther neces saa-y, that we
rnore n.eariy acquaint ourselves with whatever relates
to that science. A general knovviedgc is a good pre-
paration, and enables us to proceed with ease and ex-
pedition in whatever branch of learning we apply to.
But then in the minute and intricate questions of any
science, we are by no means quaiiiied to reason with
advantage; until we have perfectly m.astered the sci-
ence to which they belong ; it being hence chiefly
that we are fm-nished \\ith those intermediate ideas,
v/hich lead to a just and successful solution.
Sec. VII. — IV/nj Mtithematicians sometimes answernot
the escjieciadon their great learning raises.
And here, as it comes so naturally in my way, I
cannot avoid taking notice of an observation that is
frequently to be met with, and seems to carry in it at
first sight something very strange and unaccountable.
It is, in short, this, that mathematicians, even such as
are allowed to excel in their own profession, and to
have discovered themselves perfect masters in the art
of reasoning, have not yet been always happy in treat-
ir2 DUNCAN'S ELEMENTS
mg upon other subjects ; but rather fallen short, not
only what might naturally have been expected from
them, but of many writers much less exercised in the
rules of the argumentation. This will not appear sl»
very extraordinary, if we reflect on what has been
hinted above. Mathematics is an engaging study :
sTid men who apply themselves that way, so wholly
plunge into it, that they are for the most but little ac-
quainted with other branches of knowledge. Vv hen,
therefore, they quit their favorite subject", and enter
upon others, that are in a manner new and strange to
t'nem, no wonder if they find their invention at a stajid.
Because, however perfect they may be in the art of
jeasoning, yet wanting here those intermediate ideas
Vi^hichare necessary to furnish out a due train of pro-
positions, ail their skill and ability fails them.. For a
bare knowledge of the rules is not sufficient. V/e
must farther have materials whereunto to apply them.
And when these are once obtained, then it is that an
able reasoner discovers his superiority, by the just
choice he n.akes, and a certain masterly disposition,
that in every step of the procedure carries evidence
iiud conviction along with it. And hence it is, that
Euch mathematicians as have of late years applied
themselves to other sciences, and not contented v/ith
a superficial knowledge, endeavoured to reach their
inmost recesses ; such mathematicians, I say, have,
by mere strength of mind, and a happy application of
geometrical reasoning, carried their discoveries far
beyoi;d what was heretofore judged the utm.ost limits
©f human knovviedge. This is a truth abundantly
knov/n to all who are acquainted with the late won-
eleixad in:iproyenient£ in natural philosophy.
OF LOGIC. 173
Sec. VIII. — Secondhj, the Skill of applyhig Intermediate
Ideas happily in particular instances.
I come liow to the second thing required, in order
to a successful progress in rer^scning, namely, the skill
and talent of applying intermediate ideas happily in
all particular instances that come under consideration.
And here I shall not take up much time in laying
down rules and precepts, because I am apt to think
they would do but little service. Use and exercise
are the best instructors in the present case : and
Avhatever logicians may boast, of being able to form
perfect reasoners by book and rule, yet we find by^
experience, that the study of their precepts does not
Lhvays add any great degree of strength to the un-
derstanding. In short, 'tis the habit alone of reason-
ing that makes a reasener. And therefore the true
Avay to acquire this talent, is, by being much conver-
sant in those sciences vrhere the art of reasoning is
allowed to reign in the greatest perfection. Hence it
was, that the ancients, v/ho so well understood the
manner of forming the mind, always began with
mathematics as the foundation of their philosophical
studies. Here the understanding is by degrees hab-
ituated to truth, contracts insensibly a certain fond-
ness for it, and learns never to yield its assent to any
proposition, but vvhere the evidence i» sufficient to
produce full conviction. For this reason Flato has
called mathematical demonstrations the cathartics or
purgatives of the soul, as being the proper means to
cleanse it from error, and restore that natural exer-
cise of its faculties in which just thinking consists. And
indeed I believe it will be readily allowed, that no sci-
ence furnishes so many instances of a happy choice
of intermeaiate ideas, and a dextrous application of
them, for the discovery of truth and enlargement of
knowledge.
174 DUNCAN'S ELEMENTS
Sec. IX. — The Study of Mathematical Demonstrations
of great avail in this 7-e&pect.
If, therefore, we would form our minds to a habit
of reasoning- closeiy and in train, we cannot take any
iT.vore certain method, than the exercising ourselves
in mathematical demxonstrations, so as to contract a
kind of familiarity with them ; " not tliat we look up-
on it as necessary, fto use the wurds af the great
Mr. Locke) that all men should be deep mathema-
ticians, but that, having got the way of reasoning
which that study necessarily brings the mind to, they
may be able to transfer it to other parts of knowledge,
as they shall have occasion. For iii ail sorts of reas-
oning every single argument should be managed as a
mathematical demonstration, the connexion and de-
pendence of ideas should be followed, till the mind is
brought to the source on which it bottoms, and can
trace the coherence through the whole train of proofs.
It is in the general observable, that, the faculties of
our souls are improved and made useful to us just af-
ter the same manner as our bodies are. Would you
have a man v/rite or paint, dance or fence v/ell, or
perform any other m^anual operation, dextrous] y and
with ease ? Let him have ever so much vigour and
activity, suppleness and address naturally, yet no body
expects this from him, unless he has been used to it,
and has employed time and pains in fashioning and
forming his hand, or outward parts to these motions.
Just so it is in the niind ; would ycu have a man reas-
on v»^eii, you must use him to it betimes, eiicrcise his
mind in observing the connexion of ideas, and follow-
ing them in train. Nothing does this better than math-
ematics ; which, therefore, I think should be taught
all those who have the time and opportunity, not so
much to make them mathematiciar<s, as to make
them reasonable creatures j for though we all call
OF LOGIC. irs
ourselves so, because we are born to it, if we please ;
yet we may truly say, nature gives us but the seeds of
it. We are born to be, if we please, rational creatures ;
but 'tis use and exercise only that makes us so, and
we are indeed so, no faniier than industry and appli-
cation has carried us." Conduct of the Underaianding.
Sec. X. — As also of -^uch Authors on other Subjects^ cs
are distin^uUhcd fur Strerigth and Justnesis cf Reas-
oning:
But although the study of mathematics be, of all
others, the most useful to form the mind and "-ive it
an early relish of truth, yet ought not other parts of
philosophy to be neglected. For there also we meet
wiuh many opportunities of exercising the powers of
the understanding ; and the variety of subjects natur-
ally lead us to observe ail those different turns of
thinking that are peculiarly adapted to the several
ideas we examine, and the truth3%ve search after.—
A mind thus trc^ined, acquires a certain mastery over
its own thoughts, insomuch that it can range and
model them at pleasure, and call such into view as
best suit its present designs. Now in this the whole
art of reasoning consists, from am.ong a great variety
of different ideas, to single out those that are most
proper for the business in hand, an.d to lay them to-
gether in such order, that from plain and easy begin-
nings, by gentle degrees, and a continual train of evi-
dent truths, we m.ay be insensibly led on to such dis-
coveries, as at our iirst setting out, appeared beyond
the reach of the human understanding.^ For this'pur-
pose, besides the study of mathematics before recom-
mended, we ought to apply ourselves diligently to the
reading of such authors as have distinguished them-
selves for strength of reasoning, and a iust and accu-
rate m.anner of thinking. For it is observeable, that
175 DUNCAN'S ELEMENTS
a mind exercised and seasoned to truth seldom rests
satisfied in a bare contemplation of the arguments
offered by others, but will be frequently essaying its
ovrn strength, and pursuing its discoveries upon the
plan it is most accustomed to. Thus we insensibly
contract a habit of tracing truth from one stage to an-
other, and of investigating those general relations and
properties v/hich we afterwards ascribe to particular
things, according as Vv'e find them comprehended un-
der the abstract ideas to which the properties belong.
And thus having particularly shown how^ we are to
distribute the several objects of nature under general
ideas, what properties we are to ascribe to them in
consequence of that distribution, and how to trace and
investigate the properties tliemselves ; I think I have
sufficiently explained all tnat is necessary tov/ards a
due conception of reasoning, and shall therefore here
conclude this chapter.
CHAP. .IV.
OF THE FORMS OF SYLLOGISMS. .
Sec. I. — The Figures of Syllogisms.
XJ.ITHERTO we have contented ourselves with a
general notion of syllogisms, and of the parts of which
they consist. It is now time to enter a little more
particularly into the subject, to examine their various
forms, and to lay open the rules of argumentation
proper to each. . In the syllogisms mantioned in the
foregoing chapters, we may observe, that the middle
terini'A the subject of the major proposition, and the
predicate of the 7nlnor. This disposition, though the
most natural and obvious, is not, however, necessary j
OF LOGIC. -177
It frequently happening that the iriddle icrm is the
subject in both the premises, or the predicr.te inbcth ;
and sometimes, directly contrary to its di^^posltion in
the foregoing chapters, the predicate in the p^za/sr, and
the subject in the minor. Hence the distinction of syl-
logisms into various kinds, called /^;^7V5 by logicians.
Yo^fgurc^ according to their use of the word, is noth-
ing else but the order anci disposition of the irdddle
term in anv syllogism. And as this disposition is,
'vve f.ee, four-fold, so the figures of syllogisms thence
arising are four in number. V/hen the mkldle term
is the subject of the //Zu/or prGpositio:, and the prtdi-
cati: of the ininor^ we have whiU is called the firetjg-
zirc. If on the other hand, it it^ the predicate of both
thf; premises, the syllogism is said to be in the second
fl-ure. Again, in the tliirdfgnrc, the viiddle term is
t/'ie subject of the two premises. And lastly, by mak-
ing it the predicate cf the major, and sub-ect of the
minor, we obtain syllogisms in the fourth^^wrt?.
Sec, 11. The Moods of Syllogisms.
But besides this four-fold distinction of syllogisms,
there is also a farther subdivision of them in every fig-
ure, arising from the quantify and quality, as they are
called, of the propositions. By qiuintity vre mean the
consideration of propositions as universal or particu-
lar, bv quality as affirmative or negative. Now as m
sU the several dispositions of the middle term, the
propositions, of which a syllogism consists, may be
either universal or particular, affirmative or negative ;
tlie due determination of these, and so putting them
togetiier as the laws of argumentation require, con-
stitute what logicians call the ?nGods of syliogisms.—
Of these moods there are a determinate number^ to
everv ftgure, including ail the possible waysmwmch
propcsitions dinerlDg'in quaniiiy or quality canoe
178 DUNCAN'S ELEMENTS
combined, according to' any disposition of the middle
tcrm^ in order to arrive at a just conclusion. The
shortness of the present work will not allo^v of enter-
ing into a more particular description of these several
distinctions and divisions. I shall therefore content
myself witli referring the reader to the Port Royal art
of thinkings where he will find the moods diW^Jigurea
of syllogisms distinctly explained, raid the rules prop-
er to each very neatly demonstrated.
Sec. III. — Foundation of the other Dhdsio7is cf Syllo-
gis?ns.
The division of syHogiSms. according to mood and
figure, respects those especially, which are known by
the name of plain simple syllogisms; that is, which
are bounded to three propositions, all simple, and where
the extremes and middle terra are connected, accord-
ing to the rules "laid down above. But as the mind is-
not tied down to any one precise form" of reasoning,
but sometimes makes use of more, sometimes of* few-
er premises, and often takes in compound and condi-
tional propositions, it may not be amiss to take notice
of the din'jrenc forms derived from this source, and
explain the rules by which the mind conducts itself
in the use of them.
Sec. IV, — Conditio7ial Syllogisr/is.
Vv lien in any syllogism, the raojor is a conditional
proposition, the syllogism itself is termed conditional.
Thus :
If there is a God, lie ouglit to be worshipped.
But there is a God :
Therefciv he ought to be worshipped.
In this example, the mujor or first proposition, is,
we see, conditional, and therefore the syllogism itself
is ulso of the kind called by that n?.me. And here we
OF LOGIC. it^
are to observe, tliat all conditional propositions are
made up of two distinct parts ; one expressing the
condition upon vvhich the predicate agrees or disagrees
^vit■ll the -subject, as in this now before us, if there is a
God; tke other joining or disjoining the said predi-
cate and subject, as here, /le ought to be ivorshipjied.
The first of these parts, or that which implies the
condition, is called the antecedent ; the second, where
we \c>'m or disjoin the predicate and subjectf has the
name of the consequent.
Sec. V. — Ground of Illation in conditional Syllogi&ins.
These things explained, we are farther to observe,
Aat in all propositions of this kind, supposing them
to be exact in point of form, the relation between the
antecedent and consequent, must ever be true and
real ; that is, the antecedent must alv/ays contain
some certain or genuine condition which necessariiv
implies the consequent ; for otherwise, the proposition
itself will be false, and therefore ought not to be ad-
mitted into our reasonings. Hence it follows, that
when any conditioii-al proposition is assumed, if we
admit the antecedent of that proposition, avq must, at
the same tim.e, necessarily admit the consequent:
but if we reject the consequent, Vve are, in like man-
rier, bound to reject also the antecedent. For as the
antecedent always expresses some condition which
necessarily implies the truth of the consequent ; by-
admitting the antecedent, we allow of that condition,
and therefore ought also to admit the consequent. In
like manner, if it appears that the consequent ought
to be rejected,, the antecedent evidently must be so
too ; because, as we just now demonstrated, the ad-
mitting of the antecedent would necessarily imply th^
admission aiso of the consequentr
i so DUKCAN's- ELEMENTS\
Sec. YY.—'Ths tvjo Moods of Conditional Syllogism^
From: v/hat has been said, it appears, that there are-
two ways cf arguing in hypothetical syllogism, which
lead to a certain and unavoidable conclusion. For as
the major is always a conditional preposition, consist-
ing of an antecedent and a consequent ;. if the minor
admits the antecedent, it is plain, that the couvvlusion
must admit the consequent. This is called arguing
from the admisgion of the antecedent to the admi.ssion
of the consequent, and constitutes that mood or .vc)t-
c'lQS of hyfiothttical syllogisms, which is distinguisi^ed
in the scl ..ols by the name of the fnodus ponens, in::c-
much as by it the whole conditional proposition, bot\
antecedent and consequent, is established. Thus,
it God Ls infinitely v/ise, and acts with, perfect freedom, he
does r.orhingbut what is best.
But God is iaiiuitel/ wise, and acts Avith perfect fieedom :
Therefore he does nothing but what is best.
Here we see the antecedent or first part of the con-
diticnal proposition is estabiished in the minora and the
consequent or second part in the conclusion ; Avhence
the s3/riOgism itself is an example of thQ modus fionena..
But if now we on the contrary suppose, that \hQmi710r
rejects the consequent, then- it is apparent, that the
conciiiEion mnst also reject the antecedent. In this-
case we* are said to argue from the removal of the
consequent, to ihe removal of the antecedent : ar.d
the pai tlcular mood cr species of syllogism thence
arising is called.by logicians ihamodus toUc-ns ; because,
m it, both antecedent and consequerit are rejected or
taken away, as appears by the following example :
If God were not a Being of infinite goodness, neither would
he consult the iiappincss ox his creatures.
But God does consult the happiness of his creatures :.
There foi-e He is u Being-. of iu'duite goodness.
OF LOGIC. 1^1^
Sec. VII. They include all the Legitimate JVcys of
Arguing.
These two sDecies take in the v/hole class of con^
ditioiial sviloeisrws, and include all the possible ways
©f arguina; that lead to a legitimate conclusion ; be-
cause we cannot here proceed by a conta^ay process
of reasoning, that is, from the removal of the antece^
dent to the removal of the consequent, or froni the
establishing of the consequent to the establishing of
the antecedent. For although the antecedent ahvays
expresses some real condition, which, once admitted,
necessarily implies the consequent, yet it does not fol^
low, that there is therefore no other condition ; and if
so, then, after removing the atitecedent, the conse»^
queht mav stiU hold, because of some oth.er determw
ncition that infers it. When we say : If a stone is
exposed sovie time to the rays of the sun, it vMl contract
a 'certain degree of heat ; tiie proposition is certainly
true, and, admitting the antecedent, v/e must also ad-
mit the consequent. But as th^ire are ocher ways by
which a stone may eiatherheat, it will not follow from,
the ceasing of the '^before-iiientioned condition, that,
therefore the consequent cannot take place. In oth-
er words, we cannot argue, but the stone has not beem
exfiQsed to the rays of the sun ; therefore neither has it
arry degree of heat ; inasmuch as there are a great
m-j-»y other wavs by which heat might have been;
communicated to it. And if we cannot argue fi'oni.
the removal of the antecedent to the removal of the
ccnseouent, no more can we from the admission of
the coVisequent to the admission of the antecedent.
Eecause, as the consequent may flow from a great
variety of different suppositions, 'the allowing of it.
does not determine the precise supposition, but only
that som-e of them must take place. Thus in the
fore3:oing propcGiticns, if a stont is ex hosed muie tuns'
1S2 DUNCAN'S ELEMENTS
to the rays of the sunlit will contract a certain degree of
heat : admittmg the consequent, viz. that it has con-
tracted a certain degree of heat, \ve are not therefore
bound to admit the antecedent, that it has been some
time expQficd to the rays of the sun ; because there are
many other causes whence that heat may have pro-
ceeded. These two v/ays of art^uing, tlierefore, hold
not in conditional syllogisms. Indeed, vvhere the an-
tecedent expresses the only condition on which the
consequent takes place, there they may be applied
"nith safety \ because, wherever that condition is not,
we are sure that neither can the consequent be, and
so may argue from tiie removal of the one to the re-
moval of the other ; as, on the contrary, wherever the
consequent holds, it is certain that the condition must
£lso take place ; which shows, that by establishing the
consequent, we at the same time establish the ante-
cedent. But as it is a very particular case, and that
happens but seldom, it cannot be extended into a gen-
eral rule, and therefore affords not any steady and
universal ground of reasoning upon the two forego-
ing suppositions.
Sec. VIII. — Ttie Manner of Arguing- in Disjunctive
Syllogisins.
As from the major^s being a conditional proposition,
we obtain the species of conditional syllogisms ; so
where it is a disjunctive proposition, the syllogism, to
■which it belong-s, is called disjunctive, as in the fo!'-
Icwing example :
The world is either self-existent, or the work of some nnite
or of some infinite being.
But it is npt self-e.\istent, nor the work of a finite being :
Therefoi-e it is the work of an infinite being.
Now a disjunctive proposition is that where of sev-
eral predicates v/e affirm one necessarily to belong to
OF LOGIC. 183*
the subject, to the exclusion of all the rest, but leave
that particular one undetermined. Hence it follows,
that as soon as we determine the particular predicate,
ail the rest are of course to be rejected ; or if we re-
ject all the predicates but one, that one necessarily
takes place. When, therefore, in a disjunctive syllo-
gism, the several predicates are enumerated in the
major — if the mijior establishes any one of these pre-
dicates, the conclusion ougiit to remove all the rest ;
or if, in the minor^ all the predicates but one are re-
moved, the conclusion must necessarily establish that-
one. Thus in the disjunctive syllogism given above,
the major affirms one of three predicates to belong to
the earth, viz. self-existence^ or that it is the ivorkofa
jiy-iite^ or that it is the work of an infinite being. Two
of these predicates are removed in the minor, viz. self-
e.riste7ice, and the ivork of a finite being. Hence the
conclusion, necessarily ascribes to it the third predi-
cate, and affirms, that it is the ivork of an infinite being.
If now we give the syllogism another turn, insomuch
that the minor may establish one of the predicates,
by affirming the earth to be the prcdicction of a?! infi-
nite being — then the conclusion must remove the other
two, asserting it to be neithei* self-exist etU, nor the
Kvork of a finite being. These are the forms of reas-
oning in this species of syllogisms, the justness of
which appears at first sight ; and that there can be no
ether, is evident fram the very nature of a disjunctive
proposition.
Sec. IX. — Imperfect or mniilated Syllogisms.
In the several kinds of syllogisms hitherto men-
tioned, we may observe, that the pai'ts are complete ;
that is, the three propositions of wjiich they consist
are represented in form. But it often happens, that
some one of the premises is not only an evident truth,
;]S4 DUNCAN'S ELErvIENTS
but also familiar, and in tlie minds of all men ; in which
case it is usually omitted, whereby we have an impei^
feet syllogism, that seems to be made up of only two
propositions. Should we, for instance, argue m this
manner:
Every man is' morta] ;
' Therefore every king is mortal :
the syllogism appears to be imperfect, as consisting
but of two propositions ; yet it is realiy complete, only
the imnor [evsjy king" is a wan'\ is omitted, and Jeft to
the reader to supply, as being a proposition so familiar
and evident, that it cannot escape him.
Sec. X. — Enthymemcs.
These seemingly imperfect -syllogisms are called
Enthymemes^ and occur very frequently in reasoning,
especially v^^here it makes a part of common conver-
sation. Nay, there is a particular elegance in them,
because not displaying the argument in all its parts,
they leave somewhat to the exercise and invention of
the mind. By this means we are put upon exerting
ourselves, and seem to share in the discovery of v/hat
is proposed to us. Now this is the great secret of fine
writing, so to franiQ and put together our thoughts,
as to vrive full play to the render's im.agination, and
draw him insensibly into our very views and course of
reasoning. This gives a pleasure not unlike to that
which the author himself feels in composing-. It be-
sides shortens discourse, and adds a certain force and
liveliness to our arguments, vrhen the words in v/hich
they are conveyed, favor the natural quickness of the
mind in its operations, and a single exprefision is left
to exhibit a -.'hcle train of thouglits.
OF LOGIC. iS5
-Sec. W.—^Ground of Reasoning in imvicdiats Ccncc-
que7ices.
But there is another vspecies of reasonin^j with two
'propositions, which seems to be complete in itself, and
'where we admit the conclusion, without supposinp: anv
tacit or suppressed judgment in tlie mind, f';om wh.icli
it follows syiogistically. This happens between pro-
positions where the connexion is such, that the ad-
mission Oi'' the one, necessarily, and at tlie first sight,
implies the admission also cf the otiier. For if it so
falls cut, that the proposition, en which the other de-
pends, is self-evident, we content ourselves with bare-
ly ainrming it, and infer that other by a direct ccnclu-
s'on. Thus, by admitting an universal proposition,
we are forced also to adniitcf all the particular prono-
sitions comprehended under it, this being- tlie very
condition that constitutes a proposition universal. If
Ihen that universal proposition chances to 1>3 self-evi-
dent, the particular ores follow of course, without any
farther train of reasoning-. Whoever allovrs, for in-
"Etance, that things equal to cm and the sar.ie thing are
equal to one another^ must at the same time allow, thc^
trjo trianglca^ each equal to a square^ whose side is three
inches^ are also equal between themselves. This argu-
ment therefore.
Things equal to one and the same tiling, are equal to cne
another ;
Thei-cicre those tw-'o triangles, each equal to the squai-e of a
line cf three inches, are equal between themselves,
is complete in its kind, and contains all that is neces-
sary towards a just and legitimate conclusion. For
the first or universal proposition is self-evident, and
therefore requires no farther proof. And as the truth
of the particular is inseparably connected with that of
the universal, it follows from it by an obvious and un-
avoidable consequence.
Z
186 DUNXAN's ELEMENTS
Sec. XII. ''111 reducible to Syllogisms of seme one form
or other.
No^v in all cases of this kind where propositions are
deduced one from another, on account of a known
and cvidcint connexion, we are said to reason by im-
mcdiaie con^ieqiitnce. Such a coherence of propositions,
manifest at first sight, and forcing itself upon the mind,
frequently occurs in reasoning. Logicians have ex-
plained a.t some length, the several Suppositions upon
which it takes place, and allow of all imraediatc conse-
fjuences that follovv' in conformity to them. It is, how-
ever, observable, that these a.rgumeriLS, though seem-
ingly complete, because the conclusion follows neces-
sarily from the single proposition that goes before,
may yet be considered as real enthymemes^ whose
■major^ which is a conditional proposition, is wanting.
The syllogism but just mentioned, when represented
according to this view, will run as follows :
If things equal to o le and the same thing are equal to one
auuiher ; these two triangles, each equal to a square whose
tide is three inches, are alio equal between themselves.
But things equal to one and the same thirg, are equal to '
one another :
Therefore also these triangles, occ. are equal between them-
selves.
This observation will be found to hold in all im-
mediate consequences whatsoever, insomuch that
they are in fact no more than enthyraemes of hypo-
thetical syllogisms: But then it is particular to them,
that tne ground, on which the conclusion rests, name-
ly, its coherence with the minor, is of itself apparent,
and seen immedia.tely to flow from the rules and
reasons of logic. As it is, therefore, entirely unne-
cessary to express a self-evident connexion, the major,
-'vhose office that is, is constantly om.itted ; nay, and
seems so very little needful to enforce the conclusion,
OF LOGIC. 187
as to be accounted commonly no part of the argument
at all. It mu5t indeed be owned, that the foree-oiny
immediate consequence might htive been reduced io
a simple, as well as an hypothetical syllogism. Tliis
will be evideDt to any one who gives himself the
trouble to make the experiment. But it is not my
design to enter farther into these niceties, what has
been said sufficing to show, that all arguments con-
sisting of but tv>o propositions, are real enthymemes,
and reducible to complete syllogisms of some one
form or other. As, therefore, the ground on which
the conclusion rests, must needs be alvrays the same
v.ith that of the syllogisms to which they belong, we
have here an universal criterion, whereby at all times
to ascertain the justness and validity of our re^soijings
in this way.
Sec. XIII.— .i Sori^cj of fikdn divjile Syllogisms.
The next species of reasoning v/e shall take notice
of here, is what is commonly known by the name of
a sorites. This is a way of arguing, in which a great
number of propositions are so linked together, ihat
liie Dredicate of one becomes continually the subject
of ffe next following, until at last a conclusion is
formed, by bringing together the subject of the first
proposition and the predicate of the last. Of thi:»
kind is the follov/iny: arc^ument :
God is OiTiiiipotent:.
An oiiinipotent being can do every thin^ possible.
He tha'- can do every thing possible, can do whatever in-
volves not a contradiction.
Tlierefore God can do whatever involves not a contradiction.
I'his particular combination of propositions may
be continued to any length vre please, without in the
least weakening the ground upon which the conclu-
sion rests. The reason is, because the sorites itself
188 DUNCAN^s ELEMENTS
may be resolved into as many simple syllogisms aa.
there are midcile terms in it ; where this is ioimd ii-
p.iversally to hold, that when such a resolution is.-
made, and the syilogisnis are placed in train, the
conclusion of the last in the series is also the conclii-
h'lon fif the sorites. This kind of argument, there-
ibre, asit serves to unite several syllogisms into one,
must stand upon the same foundation v/ith the syllo-
^^isms of which it consists ; and is, indeed, properly
speaking, no other than a compendious way of reas-
oning syilogistically. Any one muy be satisfied of
this at pleasure, if he but takes the trouble of resolv-
ing the foregoing sorites into two aistinct syliogisms.
For he wiii there nnd, that he arrives at the same
conclusion, and that, too, by the very same train of
thinking, but with abundantly more words, and the.
addition of two superfluous propositions.
Sec. XIV. — ^ Sorites of Hyjiothctical Syllogisms,
What is here said of plain sim^ple propositions, m.ay
bewail applied to those that are conditional ; that is,
any number of them may be so joined together in a
series, that the consequent of one, shall becom^ con-
tinually the antecedent of the next following ; in which
case, by establishing the antecedent of the first propo-
sition, we establish the consequent of the last, or by
removing the last consequent, remove also the first
antecedent This way of reasoning is exem.piified in
the following argument :
If we love any persoa, all einotlons of hatred towards him
cease.
If all emotior.s o£ hatred towards a person cease, we cannot
rejoice in hisMxiisfortunes.
If we rejoice not in his misfortunes, we certainly wishhiiHi
no injury.
Therefore if we love a person, v.e yAz\\ lii-.iiiia iKJury.
OF LOGIC. i&^
It is evident that this sorites, as well as the last, may-
be resolved into a series of distinct syllogisms, v.itli
this onlv difference, that here the syllogisms are all-
conditional. But as the conclusion of the last syllo^
«-ism i'l the series is the same v>ith the conclusion ot
the sorites, it is phiin, that this also is a compendicus
vrav of reasoniniXj whose evidence arises iVoni the evi-
dence of the several single syllogisms into which- it
TA?.y be resolved.
Sec. XV.— r/.e Growid of Reasonhig by Induction.
I come now to that kind of argument, which logi-
cians call inauction ; in order to the riglit understand-
ing of which, it wiii be necessary to observe, tb.at our
general ideas are for the most part capable of various
subdivisions. Thus the idea of the lowest species
mav be subdivided into its several individuals ; the
idea of any j-cnus, into the different species it com-
prehends ; and so of the rest. If then we suppose
this distribution to be duly made, and so as to take,
in the v>'hoie extent of the idea to which it belongs ;
then it is plain, that all the subdivisions or parts of
any idea tsiken together constitute that whole idea. —
Thus the several iivdividuals of any species taken to-
gether constitute the whole species, and all the various.
Ss'ccies comprehended under any genus, make up the
whole genus*. This being allov/ed, it is apparent, that
v/hatsoever may be afhrmed of all the several subdi=
visions and classes of any idea, ought to be affirmed
of the whole general idea to which these subdivisions
belong, ^^'hat may be affirmed of all the individuals
of anv" species, may be affirmed of the vv-hole species y
and what may be 'affirmed of all tlie species of any
genus, may also be afnrm.ed of the v,4iole genus ; be-
cause all the individuals, taken together, are the sam.e
witli the species, and all the species taken togetheri
the same with the genus...
190 DUNCAN'S ELEMENTS
Sec. XVI.— 77;^ Form and Structure cf an Argument
by Indue tic7i.
This way cf arguir^c;, where we infer universally
coRcernin- any idea, what we had before affirmed or
denied separately, of all its several subdivisions and
parts, is called reasoning by indnciion. Thus if v/e
suppose the whole tribe of animals, subdivided into
men, beasts, birds,- insects, and fishes, and then reason
concerning them after this manner i Ml mtn have a
iiOtvsr of bcginnirtg motion ; all beasts^ birdsy and in-
sects^ have ajiower af beginning raoiion ; allji-shes have
apG-VcV of beginning mo'ion ; thtrfure all ani?nals have
apo^cr cf beginning v-ction: The argument is an z>>
due don. When the subdivisions are just, so as ta
take iii the whole general idea, and the ejiumeration
is perfect, that is, extends to all and every of the in-
ferior classes or parts ; there the induction is com-
plete, and the manner of reasoning by induction is ap-
parently conclusive.
Sec. XVII. — The Ground cf Argumcntaticn in a Di-
lemma.
The last species of syllogisms I shall take notice of,
in this chapter, is that commonly distinguished by the
name of a dileimna. A dilemma is an argument by
which Y.-e endeavour to prove the absurdity or false-
hood of some assertion. In order to this we assume
a conditional proposition ; the antecedent of which is
the assertion to be dispro^ved and the consequent a
disjunctive proposition, enumerating' all the possible
suppositions upon which that assertion can take place.
If then it appeals, that ail these several suppositions
ought to be rejected, it is plain, that the antecedent,
or assertion, itself, must be so t^jo. When, therefore.
iiuch a proposition as liiat before mentioned- is m?.de
OF LOGIC. 191
the major of any syllogism — if the 7ninor rejects all
the suppositions contained in the consequent, it fol-
lows necessarily, tnat the ccncliisicn ought to reject
the antecedent, which, as v/e have said, is the very
assertion to he disproved. This particular way of
arguing:, is that which logicians call a diUir.ma ; and
from the account here given of it, it appears, that we
may in general dehne it to he ^w hirfwthctical fiyllo-
gc'sm, Tjhere the conseqiimt of the major is a disjunctive
proiiosition^ which is ivholbj taken away vr removed ia
the minor. Of this kind is the following :
If God did not create the world perfect in its kind, it niust
eitlier proceed from want of inclination, or from want of
pover.
Bu; it could not proceed either from want of inclination, or
from wan: of pov.er.
Therefore he created the world perfect in its kind. Or^
ivhicb is the same tbivg : 'Tis absurd to say that he did not
create the world perfect in \lz !:ind.
Sec. XVIII. — An imiversal Descrijitiuu of it.
The nature tiien of a dilemma is universally this.
The m^ajor is a conditional proposition, whose conse-
quent contains ail the several suppositions upon which
the antecedent can take place. As, therefore, these
suppositions are wholly removed in the minor., it is evi-
dent, that the antecedent m-ust be so Xqq ; insomuch
that v/e here ahvays argue from the removal of the
consequent to the removal of the antecedent. That
is, a dihw.ma is an argument, in the T,f.odiis tolkns of
hypothetical syilogisms, as logicians love to speak.
Hence it is plain, that if the antecedent of the mnijor
is an atHrmative proposition, the conclusion of the di-
lemma will be negative ; but if it be a negative propo-
sition, the conclusion v.ill be affirmative. I cannot
dismiss the subject without observing, that as there is
something very curious and entertaining in the struc-
-i92 DUNCAN'S ELEMENTS
ture of a dllonma^ so is it a manner or reasoning {hiVt
occurs frequently in mathematical demoriStratioiis.
Nothing is more common v/ith Euclid^ when about to
show the e(]uaiity of two given figures, or, which is
the same thmg, to prove the absurdity of asserting
them unequal ; nothing, I say, is more common with
him, than to assume, that if the one is not equal to the
other ^ it must he either greater or less-: arrd having des-
troyed both these suppositions, upon which alone the
assertion can stand, lie tr»ence very naturally infers,
that the assertion itself is false. Nov/ this is precise-
ly the reasoning of a, 6^//c7/;;/t«, and in every step coin-
cides with the frame and ccmposition of that argu=
meiit, as we have described it above.
CHx\P. V.
0? de:ionstratiok.,
Ser. ^.—-OfRea'-'.ning by a Con-catenation of SyUogisms.
AviT.^G dispatched what seemed necessary to be
id v/ith regard to the forms -of syllogisms, we now
H
proceed to supply their use and application m reason
ing. We have seen, that in ail the different appear-
ances they put on, we still arrive at a just and legiti-
mate conclusion. Now it often happens, th?ct the con-
clusion of one syllogism becomes a previous propo-
sition in another, by which means great numbers of
them are sometimes linked together in a series, and
truths are made to follow one another in train. And
as in such a concatenation of syllogisms, all the vari-
ous wa);s of reasoning that are truly conclusive, may
be with safety introduced ; hence it is plain, that in
deducinp- any truth from its f.rst principles, especially
OF LOGia 193
^^hen it lies at a considerable distance from th era, we
are at liberty to combine all the several kinds oi ar-
guments above explained, accordmg as they are lound
best to suit the end and purpose of our enquiries.
"When a proposition is thus, by means of syllogisms,
collected from others more evident and known, it is
said to he proved ; so tnatwe may in the general de-
fine r/ie proof of a propositio?!, to be a syllogism, or
series of syllogisms, coUectmg that proposition from
kno^^^l and evident truths. But more particularly, if
the syllogisms, of wh ch the proof consists, admit of
rio premises but definitions, self-evident truths, and
propositions already established, then is the argument
so constituted called a demonstration ; Avhereby it . p-
pears, that demonstrations are ultimately foundeQ on
definitions and self-evident propositions.
Sec. II. ^// Syllogisms '^v/iat soever Reducible to the
frst Figure.
But as a demonstration oft-times consists of along
chain of proofs, where all the various ways of argu-
ing have place, and where the ground of evidence
must of course be different in different parts, agree-
ably to the form of the argument made use of ; it
may not perhaps be unacceptable, if we here endeav-
our to reduce the evidence of demonstration to one
simple principle, whence, as a sure and unalterable
foundation, the certainty of it may in all cases be de-
rived. In order to this we must first observe, that
all syllogisms whatsoever, whether compound, multi-
form, or defective, are reducible to plain simple syl-
logisms in some one of the four figures. But this
is not all. Syllogisms of the first figure in particu-
lar admit of all possible conclusions : that is, any
proposition whatsoever, whether an universal afiirma
tivej or universal negative, a particular afiirmative or
A 2
194 DUNCAN^s ELEMENTS
particular negative, (which four-fold division, as we
have already demonstrated in the second part, em-
braces all their varieties) any one, I say, of these may
be inferred, by virtue of some syllogism in the first
figure. ^By this means it happens, that the syllo-
gisms of all the other figures are reducible also to
syllogisms of the first figure, and may be considered
as standing on the same foundation with them. We
cannot here demonstrate and explain the manner of
this reduction, because it would too much swell the
bulk of this treatise. It is enough to take notice, that
the thing is universally known and allowed among
logicians, to whose writings we refer such as desire
farther satisf^iction in this m.atter. This then being
laid dov/n, it is plain, that any demonstration whatso-
ever may be considered as composed of a series of
syllogisms, all in the first figure. For since all the
syllogisms, that enter the demonstration, are reduced
to syllogisms of some one of the four figures, and
since the syllogisms of all the other figures are farth-
er reducible to syllogisms of the first figure, it is ev-
ident, that the whole demonstration may be resolved
into a series of these last syllogisms. Let us now, if
possible, discover the ground upon which the conclu-
sion rests, in syllogisms of the first figure ; because,
by so doing, we shall come at an universal principle
of certainty, whence the evidence of all demonstra-
tions, in all their parts, may be ultimately derived.
Sec. Wl.-^The ground of ReasoJiing in the first Figure,
The rules then of the first figure are briefly these.
The middle term is the subject of the major proposi-
tion, and the predicate of the minor. The major is
ahvays an universal proposition, and the minor always
afiirmative. Let us now see what effect these rules
will have in reasoning. The major is an universal
OF LOGIC. 195
proposition, of which the middle term is the subject,
and the predicate of the conclusion the predicate.
Hence it appears, that in the inajor^ the predicate of
the conclusion is always affirmed or denied universally
of the middle term. Again, the minor is an affirma-
tive proposition, whereof the subject of the conclusion
is the subject, and the middle tervi the predicate.
Here then the middle term is affirmed of the subject of
the conclusion : that is, the subject of the £onclusi':.n is
affirmed to be comprehended under, or to make a
part of the middle term. Thus then we see what is
done in \.\\q previises oi 2l syllogism of the first figure.
The predicate of the conclusion is universally affirmed
or denied of some idea. The subject of the conclusion
is affirmed to be, or to make a part of that idea.
Hence it naturally and unavoidably follows, that the
predicate of the conclusion ought to be aflirmed or de-
nied of the subject. To illustrate this by an exam-
ple, we shall resume one of the syllogisms of the first
chapter :
Every creature, possessed of reason and liberty, is account-
able for his actions.
Tvlan is a creature possessed of reason and liberty :
Therefore man is accountable for his actions.
Here, in the first proposition, the predicate of the
conclusion, accountableness, is affirmed of all creatures
that have reason and liberty. Again, in the secord
proposition, ma7r, the subject of the conclusion, is
affirmed to be, or to make a part of this class of crea-
tures. Hence the conclusion necessarily and una-
voidable follows, viz. that man is accountable for his
actions. I say this follows necessarily and unavoida-
bly. Because, if reason and liberty be that which
constitutes a creature accountable, and man has reason
and liberty, it is plain he has that which constitutes
him accountable. In like manner, where the ?najpr is
196 DUNCAN'S ELEMENTS
^ negative proposition, or denies the predicate of the
conclusion universally of the middle term ; as the mi-
nor always asserts the subject of the conclusion to be
or make a part of that middle term, it is no less evi-
dent, that W'i^ predicate of the conclusion ought in this
case to be denied of the subject,. S© that the ground,
of reasoning, in ail syllogisms of the first figure, is
manifestly this : Whatever may be affirmed universal-
Ly of any idejy may be affirmed of even/ or any mmibev
of particulars comprehended under that idea.. And-
again : Whatever may be denied universally of any
idea., may be in like manner denied of every or any num-
ber cf its individuals. These tv/o propositions are
called by logicians the dictum de omni, and dictum de
mdlo, and are indeed the great principles of syllogist-
ic reasoning ; inasmuch as all conclusions whatsoev-
er, either rest immediately upon them, or upon prop--
ositions deduced from them.. But what adds greatly
to their value is, that they are really self-evident truths,
and such as we cannot gainsay, without running into
an express contradiction. To affirm, for mstance,
that no man is perfect., and yet argue that some men are
perfect ; or to say that all men are mortal., and yet
that some men are not mortal., is to assert a thing to be.
and not to be at the same time.
Sec. IV. — ^Demonstration., an Infallible Guide to Truth-
and Certainty.
And now I think we are sufficiently authorized to
affirm, that in all syllogisms of the first figure, if the
/ remises are true, the conclusion must needs be true.
If it be true that the predicate of the co«c/z^5?g;7, wheth-
er affirmative or negative, agrees universally to some
idea — and if it be also true, that the subject of the con-
clusion is a part of or comprehended under that idea;
taen it necessarily follows,. that the predicate of the-
OF LOGIC. i9r
conclusion agrees also to the subject. For to assert the
contrary, would be to run counter to some one of tLc
two principles before established ; that is, it would be
to maintain an evident contradiction. And thus vre
are come at last to the point we have been all along
endeavouring to establish, namely, that every propo-
sition, which can be demonstrated, is necessarily true.
For as every demonstration may be resolved into a
series of syllogisms, all in the first figure, and as in
any one of these syllogisms, if the prem.ises are true,
the conclusion must needs be so too : it evidently fol-
lows, that if all the several premises are true, all the.
several conclusions are so, and consequently the con-
clusion also of the last syllogism, which is always the
proposition to be demonstrated. Now that aJl the-
premises of a demonstration are true, will easily ap-
pear, from the very nature and definition of that form
of reasoning. A demonstration, as we have said, is
a series of syllogisms, all whose premises are either
definitions, self-evident truths, or prapositions already
established. Definitions are identical propositions,
wherein we connect the description of an idea with
the name by which we choose to have that idea call-
ed ; and thei^fore as to their truth there can be no
dispute. Self-evident propositions appear true of
themselves, and leave no doubt or uncertainty in the
mind. .Propositions before established, are no other
than conclusions, gained by one or more steps from
definitions and self-evident principles ; that is, from
ti'ue premises, and therefore must needs be true.—
Vv'hence all the previous propositions of a demon-
stration, being, we see, manifestly true, the last con-
clusion, or proposition to be demonstrated, must be
so too. So that dem.cnstration not only leads to ccr--
tain truth, but we have here a clear view of the ground
and toundation of that certamty,. 1 or as m demoa?-
isrs DUNCAN'S ELEMENTS
slrating, v/e may be said to do nothing more than
combine a series of syllogisms together, all resting
on the same bottom ; it is plain, that one uniform
ground of certainty runs through the whole, and that
the conclusions are every where built upon some one
of the two principles before established, as the founda-
tion of all our reasoning. These two principles are
easily reduced into one, and may be expressed thus ;
IVhatever firedicate^ luhether affirmative or negative;
agrees universally to any idea^ the &a?7ie must needs c--
gree to every or any number of imfividuals comfirehend-
ed under that idea. And thus at length we have, ac-
cording to our first design, reduced the certainty of
demonstration to one simple and universal principle
which carries its own evidence along with it, and
which is, indeed, the ultimate foundation of all syllo-
gistic reasoning.
bee. V. — -The rides of Logic furnish a sufficient criteiion
for trie distinguishing between Truth and Falsehood,
Demonstration, therefore, serving as an infallible
guide to truth, and standing on so sure and unaltera-
ble a basis, we may now venture to assert, what I
doubt not will appear a paradox to many, namely,
that the rules of logic furnish a sufficient criterion for
the distinguishing between truth and falsehood. For
since every proposition that can be demonstrated is
necessarily true, he is able to distinguish truth from
falsehood, vrho can with certainty judge when a prop-
osition is duly demonstrated. Now a demonstration
is, as v/e have said, nothing more than a concatenation
of syllogismjsjall whose premises are definitions, self-
evident truths, or propositions previously established.
To judge, therefore, of the validity of a demonstra-
!!^"'. '^^'^ ^^^«=^ ; be able to distinguish whether the de-
finitions that enter it are genuine, and truly descrip-
OF LOGIC. 199
live of the ideas they are meant to exhibit ; whether
the propositions assumed without proof as intuitive
truths, have really that self-evidence to which they lay
claim ; whether the syllogisms are drdwn Tip in due
form, and agreeable to tlie laws of argumentation ;
in line, whether they are combined together, in a just
and orderly manner, so that no demonstrable propo-
sitions serve any v/here as premises, unless they are
conclusions of previous syllogisms. Now it is the
business of logic, in explaining the several operations
of the mind, fully to iflWfict us in all these points. It
teaches the nature and epG of definitions, and lays
dowi^the rules by which they ought to be framed. It
unfolds the several species of propositions, and di;3-
tinguishes the self-evident from the demonstrable. It
delineates also the different forms of syllogisms, and
explains the laws of argumentation proper to each.
In fine, it describes the manner of combining syllo-
gisms, so as that they may form a train of reasoning,
and lead to the successive discovery of truth. The
precepts of logic, therefore, as they enable us to judge
with certainty, vrhen a proposition is duly demonstrat-
ed, furnish a sure criterion for distinguishing betv/een
truth and falsehood.
Sec. VI. 4nd extending to all Cases ivhere a cerlcdn
Knordcdge of Truth is attainable,
■ But perhaps it may be objected, that demonstration
is a thing very rare and uncommon, as being the pre-
rogative of but a few sciences, and therefore the cri-
terion here given can be of no great use. I answer,
that wherever by the bare contemplation of our ideas,
truth is discoverable, there also demonstration may be
obtained. Now that I think is an abundantly sufiicient
criterion, which enables us to judge with certainty,
in all cases where the knowledge of truth conies with-
■;S00 DUNCAN'S ELEMENTS
in our reach ; for with discoveries that lie beyond tlic
?hiiits of the human mind, we have properly no busi-
Ticss nor concernment. When a proposition is de-
monstrated, we are certain of its truth. \Vhen, on
the contrary, our ideas are such as have no visible
connexion nor repugnance, and therefore furnish not
the proper means of tracing their agreement or disa-
c;reement, there we are sure that knowledge, scientif-
ical knowledge I mean, is not attainable. But where
tliere is some foundation of reasoning, which yet a-
mounts not to thefuUevidenceof^fmonstration, there
the precepts of logic, by teachingXis to determine a-
right of the degree of proof, and of what is still want-
ing to render it full and complete, enable us to make
a due estimate of the measures, of probability, and to*
proportion our essent to the grounds on which the
proposition stands. And this is all we can possibly
arrive at,*Gr even so much as hope for, in the exercise
cf faculties so imperfect and limited as ours. For it
were the height of folly, to expect a criterion that
should enable us to distinguish truth from falsehood,
in cases where a certain knowledge of truth is hot at-
tainable.
Sec. VII. The Distinction of Demonstration into di-
rect and indirect.
We have now done with what regards the ground
-and evidence of demonstration ; but before we con-
clude this chapter, it may not be improper to take no-
tice of the distinction of it into direct and indirect^.-^
A direct demonstration is, when beginning with defi--
nitions, self-evident propositions, or known and allow-
ed trviths, v/e form a train of syllogisms, and combme
them in an orderly manner, continuing the series
ti'iroagh a variety of successive steps, until at last we
£rr:Yt at a syllogism, whose conclusion is the propo-
OF LOGIC. 201
sition to be demonstrated. Proofs of this kind leave
no doubt or uncertainty behind them ; because all the
several pi^emises being true, the conclusions must be
so too, and of course the very last conclusion, or pro-
position to be proved. I shall not, therefore, any farther
enlarge upon this method of demonstrating ; having,
I^hope, sufficiently explained it in the foregoing pare
of this chapter, and shown wherein the force and va-
lidity of it lies. The other species of demonstration
is the indirect^ or as it is sometimes called, the afiolo-
gical. The manner of pToceeding here is, by assum-
ing a proposition v/hich directly contradicts that we
mean to demonstrate, and thence by a continued train
of reasoning, in the way of a direct demonstration,
deducuig some absurdity or manifest untruth. For'
hereupon we conclude that the proposition assumed
^vas false, and thence again, by an immediate conse-
quence, that the proposition to be demonstrated is
true. Thus Euclid^ in his third book, being to de-
monstrate, that circles vftiich touch one another inward-
ly have not the same centre ; assumes the direct con-
trary to this, viz. ttiat theij have the same centre : and
hence by an evident train of reasoning, proves, that a
iiart is equal to the ivhole. The supposition therefore
leading to the absurdity he concludes to be false, viz.
tJiat circles touciiing one another invjardly have the same
centre^ and thence again immediately infers, thai they
JuLve not the same centre.
Sec. VIIL — Ground of Reasoning in indirect Demon-
straUons.
Now because this manner of demonstration is ac-
counted by some not altogether so clear and satisfac-
tory, nor to come up to that full degree of evidence,
which v/e meet v/ith in the direct way of proof ; I
shall, therefore, endeavour here to give a particular
B 2
202 DUNCAN'S ELEMENTS
illustration of it, and to show that it equally ivith the
other leads to truth and certainty. In order to this
Ave must observe, that tvfo propositions are said to be
contradictory one of another, when that which is as-
serted to be in the one, is asserted not to be in the
other. Thus the propositions — circlef; that touch one
another inwardly have the same centre — and circles that
touch one another inivardly have not the same centre —
ai^ contradictories ; because the second asserts the
direct contrary of what is asserted in the first. jS'ow
in all contradictory propositions, this holds universal-
ly, that one of them is necessarily true, and the other
necessarily false. For if it be true, that circles, v/hich
touch one another inwardly, have not the same centre,
it is unavoidably false, that they have the same centre.
On the other hand, if it be false that they have the
same centre, it is necessarily true, that they have not
the same centre. Since, therefore, it is impossible for
tliem to be both true or both false at the same time,
it unavoidably follows, that one is necessarily true,
and the other necessarily false. This then being- al-
lowed, wiiich is indeed self-evident, if any tv/o contra-
dictory propositions are assumed, and one of them can
by a clear train of reasoning be demonstrated to be
false, it necessarily follows that the other is true.— ^
For as the one is necessarily true, and ^the other ne^
ccssarily false, v/hen we come to discover which is the
false proposition, we thereby also know the other to
be true.
Sec. IX. — Indirect Demonstrations a sure Guide to
Certainly.
Now this is precisely the manner of an indirect de-
monstration, as is evident from tiie account given of
it above. For there we assume a proposition which
directly contradicts that we m.can to demonstrate, and
or LOGIC. 205
having, by a continued series of proofs, sllo^\^l it to be
false, thence infer that its contradictory, or the pro-
position to be demonstrated, is true. As therefore
this last conclusion is certain and unavoidable, let us
next enquire, after what manner we come to be satis-
lied of the falsehood of the assumed proposition, that
so no possible doubt may remain, as to the force and
validity of demonstrations of this kind. The manner,
then, is plainly this. Beginning with the assumed
proposition, we, by the help of definitions, self-evi-
dent truths, or propositions already established, con-
tinue a series of reasoning, in the way of a direct de-
monstration, until at length we arrive at some absur-
dity or known falsehood. Thus Euclid^ in the exam-
ple before mentioned, from the supposition that cir-
cles touching one another inwardly have the same
centre, deduces, that a part is equal to the tvhols.
Since, therefore, by a due and orderly Drocess of reas-
oning, we come at last to a false conclusion, it is man-
ifest, that all the premises cannot be true. For were
all the premises true, the last conclusion must be so
too, by what has been before demonstrated. Now as
to all the other premises made use of in the course of
reasomng, they are manifest and known truths by
supposition, as being either definitions, self-evident
propositions, or truths established. The assumed
proposition is that only as to which any doubt or un-
certamty remains. That alone, therefore, can be
false, and indeed, ft^om v/hat has been already shown,
must unavoidably be so. And thus we see, that in
indirect demonstrations, two contradictory proposi-
tions being laid down, one of which is dem.onstrated
to be false, the other, which is alwavs the proposition
to oe proved, must necessarily be true ; so that here,
as well as in the direct way of proof, we arrive at a
clear and satisfactory knowledge of truth.
204 DUNCAN'S ELEMENTS
Sec. X. — A particular Case of Indirect Demoiistradrm.
This is universally the method of reasoning in all
apological or indirect demonstrations ; but there is
one particular case, which has something so singular
and curious in it, that well deserves to be mentioned
bv itself ; more especially, as the ground on v/hich
the conclusion rests will require some farther illus-
tration. It is, in short, this : that if any proposition
is assumed, from which, in a direct train of reasoning,
we can deduce its contradictory, the proposition so as-
sumed is false, and the contradictory one true. For
if we suppose the assumed proposition to be true,
then, since all the other premises that enter the de-
monstration are also true, we shall have a series of
reasoning, consisting wholly of true premises ; whence
tiie last conclusion, or contradictory of the assumed
proposition, must be true likewise. So that by this
jiieans we should have two contradictory propositions
both true at the same time, v/hich is manifestly im-
possible. The assumed proposition, therefore, vrhcnce
this absurdity flows, must necessarily be false, and
consequently its contradictory, which is here the pro-
position deduced from it, must be true. If then any
proposilon is proposed to be demonstrated, and we
assume the cojitraclictory of that proposition, and thence
directly infer the proposition to be demonstrated, by
this very m.eans we know that the proposition so in-
ferred is true. For since from an assumed propo-
sition v/e have deduced its contradictory, we are there-
by certain that the assumed proposition is false ; and
if so, then its contradictory, or that deduced from it,
which in this case is the same with the proposition to
be demonstrated, must be true.
OF LOGIC. 205
e.c XI i due Knoivlegde of the Prindtiles of Logic
indisiiensably necessary to make us proper judges of
Demonstration ;
That this is not a mere empty speculation, void of
all use and application m practice, is evident irom the
Conduct of the mathematicians, ^vho have adopted
this manner of reasoning, and given it a place among
their demonstrations. We have a curious mstance ot
it in the twelfth proposition of the ninth book ot the
elemets L:uclid there proposes to demonstrate, that
iv anv series of numbers, rising from unity in geometry
cal firoKression, all the prime numbers that measure the
I J term in the series, nvill also measure the next after
unitu. In order to this he assumes the contradictory
of the proposition to be demonstrated, namely; that
some prime number measuring the last term in tne series,
does not measure the ntxt after unity, and thence by a
continued train of reasoning proves, that it actuaUy
does measure it. Hereupon he concludes tne assum-.-
ed proposition to be false, and that vrhich is deauced
from it, or its contradictory, which is the very pi;opo-
sition he proposed to dem.onstrate, to be true. .Now
that this is a just and conclusive way of reasomng,.
is abundantlv manifest, from what we have so cieariy
established above. I would only here observe, how
necessary some knowledge of Uie rules of logic is,
to enable us to judge of the force, justness, and vaau-
ity of demonstrations ; since such may sometimes
occur, where the truth of the proposition demonstrat-
ed will neither be owned nor perceived, unless we
know before-hand, by means of logic, that a conc^lu-
sion so deduced, is necessarily true anc. valid, .or
thoup-h it be readily allowed, that by the mere strength
of our natural faculties, we can at once discern, that
of two contradictory propositions, the one is .lecessa^
206 DUNCAN'S ELEMENTS
rily true, and the other necessarily false : vet when
tney are so linked together in a demonstration, as
that the one serves as a previous proposition, whence
tne other is deduced ; it does not so immediately
appear, without some knowledge of the principles of
log.c, why that alone, which is collected by reason-"
mg, ought to be embraced as true, and the other,
whence it is collected, to be rejected as false.
Sec. ZilL^Jnd of itself sufficievd to guard us against
Error and false P.easoning.
Having thus, I hope, sufficientlv evinced the cer-
tainty^of demonstration in all its branched, and shown
theruies by which we ought to proceed, in order to
arrive at a just conclusion, according to the various
ways of arguing made use of ; I hold it needless to
enter upon a particular consideration of those several
species of false reasoning which logicians distinguish
by the name of soiiliisms. He that thoroughly under-
stands the form and structure of a good argument, -
■Nvill of nimseh readily discern every deviation from it
Arxd although sophisms have been divided into many
classes, which are all called by sounding names, that
tnerefore carry in them much appearance of learning ; '
yet are the errors themselves so very palpable and ob-
Tious, that I should think it lost labour to write for a
man capable of being misled bv them. Here, there-
tore, we choose to conclude this third part of logic,
and shall in the next book give some account of rneth^
ocf, which, though inseparable from reasoning, isnev--
ertheless always considered by logicians as a distinct
operation of the mind ; because its influence is not
conuned to the mere exercise of the reasoning facul-
ty, uut extends in some degree to all the transactions
©I the understanding.
OF LOGIC. 2or
BOOK IV.
OF METHOD.
CHAP. I.
OF METHOD IN GENERAL, AND THE DIVISION OF IT
INTO ANALYTIC AND SYNTHETIC.
Sec. L — The understanding sometimes emfiloyed hi put'
ting together known truths ;
VV E have riO'.v done with the three first operations
of the mind, whose office it is to search after truth,
and enlarge the bounds of human knowledge. There
is yet a fourth which regards tlie disposal and ar-
rangement of our thoughts, when we endeavour so to
put them together, that their mutual connexion and
dependence may be clearly seen. This is what logi-
cians call method^ and place always the last in order,
in explaining the powers of the understanding ; be-
cause it necessarily supposes a previous exercise of
our other faculties, and some progress made in knovv-i-
€dge, before vre can exert it in any extensive degree.
It often happens, in the pursuit of truth, that unex-
pected discoveries present themselves to the mind,
and those, too, relating to subjects very rem.ote from
that about Vv'hich we are at present employed. Even
the subjects themselves of our enquiry, are not al-
ways chosen with a due regard to order, and their de-
pendence one upon another. Chance, our particular
way of life, or some present and pressing views, often
prompt us to a variety of researclies, tiiat have but
2.03 DUNCAN'S ELEiVIENTS
little connexion in the nature of things. When,
therefore, a man accustomed to much thinking,
comes, after any considerable interval of time, to
take a survey of his intellectual acquisitions, he sel-
dom finds reason to be satisfied with that order and
disposition, according to which they made their en-
trance into his understanding. They are there dis-
persed and scattered, without subordination, or any
just and regular coherence ; insomuch that the sub-
serviency of one truth to the discovery of another,
does not so readily appear to the mind. Hence he
is convinced of the necessity of distributing them into
various classes, and combining into an uniform sys-
tem whatever relates to one and the same subject.
Now this is the true and proper business of method j
to ascertain the various divisions of human knowl-
edge, and so to adjust and connect the parts in every
branch, that they may seem to grow one out of an-
other, and form a regular body of science, rising from
first principles, and proceeding by an orderly concat-
enation of truths.
Sec. II. — Sometimes in the Search and Disco-very of
such as are unknown.
In this view of things, it is plain, that we must be
before-hand well acquainted with the truths we are
to combine together : otherwise how could we discern
their serveral connexions and relations, or so dispose
of them as their mutual dependence may require ?
But now it often happens, the understanding is em-
ployed, not in the arrangement and composition of
known truths, but in the search and discovery of such
as are unknown. And here the manner of proceed-
ing is very different, inasmuch as we assemble at
once our whole stock of knowledge relating to any
subject, and, after a general survey of things, begin
OF LOGIC. 209
■with examining tliem separately and by parts. Hence
it comes to pass, that whereas at our first setting
out, we were acquainted only with some of the grand
strokes and outlines, if I may so say, of truth, by thus
pursuing her through her several v.indings and recess-
es, we gradually discover those more inward and
finer touches, v.dience she derives all her strength,
symmetry and beauty. And here it is, that vvhen,
by a narrow scrutiny into things, we have unravelled
any part of knowledge, and traced it to its first and
original principles, insomuch tiiat the whole frame
and contexture of it lies open to the view of the
mind ; here, I say, it is, that, taking it the contrary
way, and beginning with these principles, v/e can so
adjust and put together the parts, as the order and
method of science requires.
Sec. III. — Illustrated by the Similitude of a Watch.
■ But as these things are best understood when illus-
trated by examples, especially if they are obvious, and
taken from common life ; let us suppose any machine,
for instance, a watch, presented to us, vvhose struc-
ture and composition v>-e are as yet unacquainted
with, but want, if possible, to discover. Tlie manner
of proceeding, in this case, is, by taking the v/hole to
pieces, and examining the parts sepamtely one after
another. "When by such a scmtiny we have tho-
roughly inform-ed ourselves of the frame and contex-
ture of each, we then compare them together, in or-
der to judge of their mutual action and influence.
By this means vre gradually trace out the inward
make and composition of the whole, and come at
length to discern, hov/ parts of such a form, and so
put together as we found, in unravelling and taking
them asunder, constitute that particular machine call-
ed a vratch, and contribute to all the several motions
C 2
210 DUNCAN'S ELEMENTS
and phenoiTiena observable in it. This dlscoveiy
being made, we can take things the contrary way,
and, beginning with the parts, so dispose and connect
them, as their several uses and structures require,
until at length we arrive at the whole itself, from tne
unravelling of which these parts resulted.
Sec. IV. — Grcund of the Analytic and Synthetic Me-
thods.
And, as it is in tracing and examining the works of
art, so it is in a great measure in unfolding any part
of numan knowledge. For the relations and mutual
iiabitudes of things, do not always immediately ap-
pear, upon comparing them one with another. Hence
vv^e have recourse to intermediate ideas, and, by means
of them, are furnished v/ith those previous proposi-
tions that lead to the conclusion we are in quest of.
And if it so happen, that the previous propositions
themselves are not sufficiently evident, we endeavour,
by nev/ middle terms, to ascertain their truth, still
tracing things backv/ard in a continued series, until
at length we arriv^e at some syllogism, where the
premises are first and self-evident principles. This
done, we become perfectly satisfied as to the truth
of a.11 the conclusions we have passed through, inas-
much as they are now seen to stand upon the iirm
and immovable foundation of our intuitive perceptions.
.\nd as we arrived at this certainty, by tracing things
backv/ard to the original principles v/hence they flow,
so may we at any time renew it by a direct contrary
process, if, beginning with these principles, we carry
the train of our thoughts forward, until they lead us
bv a connected chain of proofs, to the very last con-
clusion of the series.
OF LOGIC. 211
Sec. V. Division of Method hito Analytic and Syn-
thetic,
Hence it appears, that in disponing and putting to-
gether our thoughts, either for our own use, that the
discoveries we have made may at ail times lie open
to the review of the mind ; or, where ue mean to
communicate and unfold these discoveries to others,
there are two v/ays of proceeding, equally within cur
choice. For we may so propose the truths relating
to any part of knowledge, as they presented thera-
seives to the mind in the manner cf investigation,
carrying on the series cf proofs in a reverse order,
until they at last terminate in first principles : or,
beginning v/\lh these principles, we take the contrary
v/ay, and from them deduce, by a direct train of rea-
soning, all the several propositions we v,-i;.nt to estab-
lish. This diversity in the manner of aiiai^iging our
t/ioughts gives rise to the tv/o-fold division of method
established among logicians. For method, according
to thei.' use of the v/crd,is nothing else but the order
and disposition of our thoughts relating to any sub-
ject. Wlien truths are so proposed and put together*
as tiiey were or might have been discovered, this is
called the amd'jtic method^ or t\iG met/wd of reschuion ;
inasmuch as it traces things backvrard to their source,
and resolves loicvviedge into its first and original prin-
ciple. V/hen, on the other hand, they are deduced
from these principles, and connected according to
their mutual dependence, insomuch that the truths
first in order tend always to the demonstration of those
that fcilov/, this constitutes what we call the synthetic
TAethod^ or method cfconvlicdiion. For here we proceed
by gathering together several scattered pails of knowl-
edge, and combining' them into one whole, or system,
in "such manntr, that tlve understanding is enabled
212 DUNCAN'S ELEMENTS
distinctly to follow truth through all her different
stacces and sradations.
Sec. VI. — Called otherivise the Method ofLweiition and
the Method of Science.
There is farther to be taken notice of, in relation
to these t^vo species of method ; that the iirst has al-
so obtained the name of the method ofinveiition^ho.-
Gau.se it observ^es the order in which our thoughts
succeed one another, in the invention or discovery of
truth. The other, again, is often denomina.ted the
■method of doctrine^ or instruction, inasmuch as in lay-
ing our thoughts before others, we generally choose
to proceed in the synthetic inanner, deducing them
from their first principles. For we are to observe,
that although there is great pleasure in pursuing
truth in the method of investig ation, because it places
us in the condition of the inventor, and shews the par-
ticular train and process of thinking by which he arriv-
ed at his discoveries ; yet it is not so well accommodat-
ed to the purposes of evidence and conviction. For at
our first setting out, we are commonly unable to divine
where the analysis will lead us ; inasmuch that our
■researches are for seme time little better than a mere
groping in the dark. And even after light begins to
break in upon us, we are still obliged to m?Jiy re-
views, and a frequent compariccn of the several steps
of the investigation among themselves. Nay, when
we have unravelled the whole, and reached the very-
foundation on which our discoveries stand, all our cer-
tainty, in regard to their truth, will be found in a great-
measure to arise from that connexion we are now
able to discern betwetn them and first principles, tak-
en in the order of composition. But in the synthetic
manner of dispo -^ing our thouglits, the case is quite
different. For as we here begin widi intuitive truths,
OF LOGIC. 213
and advance by regular deductions from them, every
step of the procedure brings evidence and conviction
along vrith it ; so that in our progress from one part
of knovvledge to anotlier, we have ahvays a clear per-
ception of the grounds on which our assent rests. In
communicating therefore, our discoveries to others,
this method is apparently to be chosen, as it v/onder-
fully improves and enlightens the understanding, and
leads to an imm.ediate perception of tri^th. >\nd
hence it is, that in the following pages, we choose to
distinguish it by the name of the wzer^^oc/ ofscunce;
not only as in the use of it we arrive at science and
certcJnty, but because it is in fact the method, in
Vvhich all those parts of hmPxan knowledge, that prop-
erl v bear the name of sciences, are and ought to be de-
livered. But vre now proceed to explain these two
kinds of method more particularly.
CKAP. II.
OF THE METHOD OF INVENTION.
Sec. I. — Origin of the several Arts and Inventions of
Human Life.
15 Y the method of invention we understand such a
disposition and arrangement of our thoughts, as fcl-
lov.s the natural procedure of the understanding, and
presents them in the order in which they succeed one
another, in the investigation and discovery of truth.
Now it is plain, that to handle a subject successfully
according to this method, we have no more to do
than observe the several steps and advances of our
minds, and fairly copy them out to the viev/ of others.
And indeed it will be found to hold in gerier..!, with
2 !4 DUNCAN'S ELEMENTS
reg-arci to all the active parts of human life, especially
Avhen reduced to that which is in the schools termed
an art ; that the rules, by which ^Ye conduc,t ourselves,
are.no ether than a series of observations drav/n from
the attention of the mind to what passes, while v.e
exercise our faculties in that particular way. For
when we set about any invention or discovery, we are
always pushed on by some invvard principle, disposi-
tion, or aptitude shall I call it, which we experience in
ourselves, and which makes us believe, that the thins^
vveare in que'iit of, is not altogether beyond our reach.
We theref:;:e begin v.^ith essaying our streni^th, and
are sometimes successful, though perhaps more fre-
quently not. But -as the mind, when earnestly bent
upon any pursuit, is not easily discouraged by a few
disappcintments, v/e are only set upon renewing our
endeavours^ and, by an obstinate pei-severence, and re-
peated ti'ialsj often arrive at the discovery of what v.e
have in view. Now it is natural for a man of a curi-
ous and inquisitive turn, after.'having mastered any
part of knowledge v/ith great labour and difficully, to
set himself to examine how he happened to miscarry
in his first attempts, and by v/hat particular method
of procedure he at length came to be successful. By
thi5 means y/e discover on the one hand, those rocks
and shelves which stand most in our way, and are apt
to disturb and ch'ick our progress ; and on the other,
that more sure and certain course, vrhich if we con-
tinue in steadily, will bring us to the attainment of
what we are in pursuit of. Hence spring all the arts
£\nd inventions of human life, wliich, as we have al-
ready said, are founded upon a series of rules and ob-
servations, pointing out the true and genuine m:.nner
of arriving at any attainment. When the mind rests
satisfied in a bare contemplation of the rules, and the
reasons on which they arc founded,
OF LOGIC. 215
edge is aJied speculalive. But if we proceed farther,
aiid endeavour lo apply these rules to practice, so as to
acquire a iiabit of exerting thera on all proper occa-
sions, vv'e are then said to be p-ossessed of the art itself.
Sec. II. — rrAy in treating of the Method of hwcniion^
xve must give seme account of the Art itself
From v\-hat has been said, it appears, that, in order
distinctly to explain the method of invention, we must
take a view of the understanding, as employed in the
search and investigation of truth. For by duly at-
tending to its procedure and advances, we shall not
only discover the rules by which it conducts itself,
but be enabled also to trace out the several helps and
contrivances it makes use of, for the more speedy and
effectual attainment of its. ends. And when these
particulars are once known, it will not be difficult for
us, in laying open our discoveries to others, to com-
bine our thouglits agreeably to the method here re-
quired. Because, having nxed and ascertained the
rules of it, and being perfectly acquainted v;ith tlie
conduct and manner of the mind, v/e need only take
a view of the several truths, as tiiey succeed one anoUi-
er in the series of investigation, setthern in order be-
fore us, and fairly transcribe the appearance they
make to the understanding. Hence it is, that logi-
cians, in treating of the method of invention, have not
merely confined themselves to the laying down of oi-
rections for tlie disposal and arrangements cf our
thoughts ; but have rather explained the art itself, and
established those rules by v/hich the mind ought to
proceed in tiie exercise of its inventive pov/ers. For
they rightly judge, that if these were thorougiy un-
derstood, the other could no longer remain unknovra.
By this means it happens, that the method of inven-
tion is bacorae another -exj^i^ession for tlie art of in-
216 DUNCAN'S ELEMENTS
iwnllon^ and very often denotes the conduct and pro-
cedure of the understanding in the search of truth.— i
And as some knowledge of the principles of the art,
is in a manner absolutely necessary towards a true
conception of the rules by which we ought to govern
and dispose our thoughts in treating subjects after this
method ; we shall, therefore, follow the example of
other logicians, and endeavour to give some short ac-
count of the business of invention, and of those sever-
al helps and contrivances by which the mind is en-
abled to facilitate and enlarge its discoveries.
Sec. Ill, dttention and a Com^irehensive understand^
ing the preparatory qualifications to Invention.
It has been already observed, that v/hen the mind
employs itself in the search of unknown truths, it be-
ghis v/ith assembling at once its vv'holc stock of knowl-
adge relating to the subject, and after a general sur-
vey of things, sets about examining them separately
and by parts. Now as in this separate examination,
the number of parts continually increase upon us —
and as it is farther necessary, that we survey them on
all sides, compare them, one with another, and accu-
rately trace their mutual habitudes and respects — it is
from hence apparent, that in the exercise of inven-
tion, two things are of principal consideration. First,
an enlarged and comprehensive understanding, able
to take in the great multitude of particulars, that fre-
quently come under our notice. Secondly, a strong
liabit of attention, that lets nothing remarkable slip
its view, and distinguishes carefully ail those circum-
stances which tend to the illustrating and clearing
the subject we are upon. These are the great and
preparatory qualifications, without which it were vain
to hope, that any considerable advance could be made
in enlarging the bounds of human knowledge. Nor
OF LOGIC. 2 If
t>ught w« to esteem it a small advantage, that the>^
are in some measure in our o^ti power, and may, by
a proper cultiv ;uon, be improved and strengthened
to a degree almost beyond belief. We find by expe-
rience, that the study of mathematics in particular is
greatly serviceable to this end. Habits, ^ve ail know,
grow stronger by exercise ; and as in this science
there is a perpetual call upon our attention, it by de-
grees becomes natural to us. so as that we can pre-
serve it steady and uniform, through long and intri-
cate calculations, and that with little or no fatigue to
the understanding. But a yet more wonderful ad-
vantage, arising from the culture of the mathematics,
is this, that hereby wq in some measure extend the
dimensions of the human mind, enlarge its compass
of perception, and accustom it to wide and compre-
hensive views of things. For whereas at our first
setting out, we often find it extremely diScult to mas-
ter a short and easy demonstration and trace the con-
nexion of its several parts : yet as we advance in the
science, the understanding is seen gradually to dilate,
and stretch itself to a greater size ; insomuch that a
long and intricate series of reasoning is often taken
in with scarce any labour of thought ; and not only
so, but we can in some cases, with a single glance of
our minds, mn through an entire system of truths,
and extend our view at once to all the several links
t hat unite and hold them together.
Sec. IV. — Judicious choice cf intermediate Ideas atioih-
er great requisite in this Art.
When we are furcished v/ith these two preparatory^
qualifications, the next requisite to the discovery of
truth is, a judicious choice of intermediate ideas. We
have seen, in the third part of this treatise, that many
of our ideas are of such a nature as not to discover
D 2
218 DUNCAN'S ELEMENTS
these several habitudes and relations by any imme-
diate comparison one with another. In this case, we
must have recourse to intermediate ideas ; and the
great art lies in finding out such as have an obvious
and perceivable connexion with the ideas whose rela-
tions we enquire after. For thus it is, that we are
furnished with known and evident truths, to serve as
premises for the discovery of such as are unknown.
And indeed the whole business of invention seems,
in a great measure, to lie in the due assemblage and
disposition of these preliminary truths. For they
not only lead us, step by step, to the discovery we are
in quest of, but are so absolutely necessary in the case,
that without them it were vain to attempt it ; noth-
ing' being more certain, than that unknown proposi-
tions can no otherwise be traced but by means of some
connexion they have with such as are known. Nay,
reason itself, which is indeed the art of knowledge,
and the faculty by which we push on our discoveries ;
yet by the very definition of it implies no more, than
an ability of deducing unknown truths from principles
or propositions that are already known. Now, al-
though this happy choice of intermediate ideas, so as
to furnish a due train of previous propositions, that
shall lead us successively from one discovery to an-
other, depends in some measure upon a natural saga-
city and quickness of mind ; it is yet certain, from
experience, that even here much may be effected by
a stubborn application and industry. In order to this,
it is in the first place necessary, that we have an ex-
tensive knowledge of things, and some general ac-
quaintance vv^ith the whole circle of arts and sciences.
Wide and extended views add great force and pene-
tration to the mind, and enlarge its capiicity of judg-
ing. And if to this we join in the second place, a
more particular and intimate study of v.'hatever re-
OF LOGIC. 219
lates to the subject about v/hich our enquiries are
employed, "\ve seem to bid fair for success in our at-
tempts. For thus we are provided v.ith an ample
variety out of v.'hich to choose our intermediate ideas,
and are therefore more likely to discover some among
them that will furnish out the previous propositions
necessary in any train of reasoning.
Sec. V. Sagacity and a quickness of understanding
greatly promoted by the study of Algebra.
It is not, indeed, to be denied, tliat when we have
even got all our materials about us, much still de-
pends upon a certain dexterity and address, in sing-
ling out the most proper, and apply inQj them skilful-
ly for the discovery of truth. This iS the talent
which is known by the name of sagacity, and com-
TQonly supposed to be altogether the gift of nature.
But yet I think it is beyond dispute, that practice,
experience, and a watchful attention to the proce-
dure of our OV.TI minds, while employed in the exer-
cise of reasoning, are even here of very great avail.
It is a truth well known to those who have made any
considerable progress in the study of algebra, that an
address and skill in managing intricate questions may
be very often obtained, by a careful imitation of. the
best models. For although when we first set out
about the solution *bf equations, we are puzzled at
every step, and thmk we can never enough admire
the sagacity of those who present us with elegant
models in that way ; yet by degrees vre ourselves
arrive at a great mastery, not only in devising proper
equations, and coupling them artuiuy together, so as
from the more complicated to derive others that are
sim.ple ; but also in contriving useful substitutions, to-
free our calculations from fractions, and those intri-
cacies that arise from surds and irrational quantities..
02O DUNCAN'S ELEMENTS
Nor is it a smail pleasure attending the proseculion of
ti.is study, that we thus discern the growing strength-
of our minds, and see ourselves approaching nearer
and nearer to that sagacity and quickness of under-
-standing which we see so much admired in others,
iir.d were at first apt to conclude altogether beyond
cur reach.
Sec. VI. — Where Art and Mivagemmt are required
in the bvmief^s cf hcvtrdiui.
We have now considered those requisites to in-
dention, that have their foundation in the natural tal-
ents of the mind : and enlarged and comprehensive
understanding, a strong habit of attention, a sagacity
and Quickneiss in discerning and applying intermedi-
ate ideas. Let us next take a \iew of such other
helps, as more immediately depend upon art and
management, and show the address of the mind, in
contriving means to facilitate its discoveries, and free
it from ail unnecessary fatigue and kibour. For we
are to observe that though the capacity of the intel-
lect may be greatly enlarged by use and exercise, yet
still our views are confined within certain bounds,
beyond which a finite understanding cannot reach.
And as it often happens, in the investigation of truth,
especially v/here it lies at a considerable distance
from first principles, that the m^nber of connexions
and relaticns are so great, as n^t to be taken in at
once by the most improved understanding ; it is
therefore one gieat branch of the Lrt of invention, to
take account of these relations, as they come into
view, and dispose them in such manner, that they al-
ways lie open to" the inspection of the mind, when
disposed to turn its attention that way. By this
means, without perplexinsr ourselves with too many
consioerations at once, v/e have yet these relations at
OF LOGIC. 22 1
€ommand, when necessary to be taken notice of m
the prosecution of our discoveries : and the under-
standing thus free and disengaged, can bend its pow-
ers more intensely towards that particular part of
the investigation it is at present concerned with.
Now in this, according to my apprehension, jies the
great art of human knowledge ; to manage with skill
the capacity of the intellect, and contrive such helps
as may bring the most wide and extended objects
within the compass of its natural powers. When,
therefore, the multitude of relations increase, very
fast upon us, and grow two unwieldy to be dealt witL
in the lump, vre must combine them in different
classes, and so dispose of the several parts, as that
they may at all times lie open to the leisurely surveys
of the mind. By this means we avoid perplexity and
confusion, and are enabled to conduct our researciies
without being puzzled with that infinite crowd of par--
ticulai's, that frequently fall under our notice in long
and difiiculL investigations. For by carrying our at-
tention successively from one part to another, vre can
upon occasion, take in the whole ; and knov/ing also
the order and disposition of the parts, iTxay have
recourse to any of theni-ftt pleasure, when its aid be-
comes necessary in the course of our enquiries.
Sec. VII. in orderly disposition c^ great use in adafit^
ing objects to tke capacity of the understandiyig ;
First, then, I say, that an orderly combination of
things and classing them together with art and ad-
4i ess, brings great and otherwise unmanageable ob-
jecis, upon a level with tne pov/ers of the mind "We
have seen, in the first part of this treatise, how by
taking numbers in a progressive series, and accord-
ing to an uniform Iav\- of composition, the most bulky
and formidable collections ai'e comprehended vdth
222 DUNXAN'^s ELEMENTS
ease, and leave distinct impressions in the under-
standing. For the several stages of the progression
serve as so many steps to the mind, by which it as-
cends gradually to the highest combinations ; and as
it can carry its views from one to another, with great
ease and expedition, it is thence enabled to run over
all the parts separately, and thereby rise to a just-
conception of the whole. The same thing happens,
in all our other complex notions, especially when they,
grow very large and complicated ; for then it is that
we becom.e sensible of the necessity of establishing
a certain order and gradation in the manner of com-
bining the parts. This has been already explained,
at some length, in the chapter of the com.position and
resolution of our ideas ; where we have traced tha.
gradual progress of the mind through all the different
orders of perception, and shown, tliat the most expe-
ditious Vv^ay of arriving at a just knowledge of the
more compounded notices of the understanding, is
by g.dvancing regularly through all the intermediate
steps. Hence it is easy to perceive what advantages
must arise from a like conduct in regard to those
several relations and connexions, upon which the in-
vestigation of truth depends. For as by this means
we are enabled to bring them all within the reach of
the mind, they can each in their turns be made use
of upon occasion, and furnish their assistance tov/ards
the discovery of what v/e are in quest of. Now this
is of principal consideration in the business of inven-
tion, to have our thoughts so much under command,
that, in comparing things together, in order to dis-
cover the result of their mutual connexions and de-
pendence, all the several lights that tend to the clear-
ing the subject sve are upon, may lay distinctly open
to the understanding, so as nothing material shall
escape its view : because an oversight of this kind,
OF LOGIC. 22S
in summing up the account, must not only greatly
retard its advances, but in many cases check its pro-
gress altogether.
Sec. VIII. — Ajid enabling ^^s to firocced gradually and
ivith ease in the investigation cf Truth.
But, secondly, another advantage arising from this
orderly disposition, is, that hereby we free the mind
from all unnecessary fatigue, and leave it to fix its
attention upon any part separately, v.ithout perplex-
-ing itself with the consideration of the whole. Un-
known truths, as v/e have already observed, are only
to be traced by means of the relation between them
and others that are known. When, therefore, these
relations become very numerous, it must needs great-
ly distract the mind, were it to have its attention coi>-
tinually upon the stretch after such a multitude of
particulars at once. But now, by tlie method cf class-
ing and ordering our perceptions above explained,,
this inconvenience is wholly prevented. For a just
distribution of things, as it asce.rtains distinctly the
place of each, enables us to call any of them into
view at pleasure, when the present consideration of
it becomes necessary. Flence the mind proceeding
gradually through the several relations of its ideas,
and marking the results of them at every step, can
always pioportion its enquiries to its strength ; and
confining itself to such a number of objects as it can
take in and manage with ease, sees more distinctly
all the consequences that arise from comparing them
one with another. ^Vhen, therefore, it comes after-
wards to take a re vie v/ of these its several advances,
as by this means the amount of every step of the in-
vestigation is fairly laid open to its inspection, by ad-
justing and putting these together, in due order and
method, it is enabled at ia^t to discern the result cf
224 DUNCAN'S ELEMENTS
the whole. And thus, as before in the composition
of our ideas, so likewise here in the search and dis-
covery of truth, we are fain to proceed gradually, and
by a series of successive stages. For these are so
xAany resting places to the mind, whence to look about
it, survey the conclusions it has already gained, and
see what helps they afford, towards the obtaining of
iL>thers which it must still pass through, before it
reaches the end of the investigation. Hence it often
happens, that very remote and distant truths, which
Be far beyond the reach of any single effort of the
mind, are yet, by this progressive method, success-
ively brought to light, and that too with less fatigue
■to tile understanding than could at first have v/ell been
imagined. For although the whole process, taken
together, is frequently much too large to come with-
in the view of the mind at once ; and therefore, con-
sidered- in that light, may be said truly to exceed its
grasp ; yet the several steps of the investigation by
themselves are often easy and manageable enough, so
that by proceeding gradually from one to another,
«nd thoroughly mastering the parts as we advance,
we carry on our researches with wondrous dispatch,
and are at length conducted to that very truth, with
a viev/ to the discovery of which the inquisition itself
was set on foot.
Sec. IX. — Algebra and Arithmetic^ profierly s/ieaking-,
both Arts of Invention.
But now perhaps it may not be improper, if we en-
deavour to illustrate these observations by an exam-
ple, and set ourselves to trace the conduct and man-
ner of the mind, when employed in the exercise of
invention. There are two great branches of the
mathematics peculiarly fitted to furnish us with mod-
da in this way. Arithmetic I mean, and Algebra.
OF LOGIC. ' 225
Algebra is univcfsaily known to be the rery art and
principle of invention ; and in arithmetic, too, "sve are
frequently put upon the finding out of unkno^'^^l niim-
bers, by means of their relations and connexions with
others that are knov.n : as where it is required to
iirjd a number equal to this sum of two others, or the
product of two others. I choose to borrow my ex-
amples chiefly from this last science, boih because
they will be more within the reach of these for whom
this treatise is principally designed ; as likewise, be-
cause arithmetic furnishes the best models of a hap-
py sarjacity and management, in classing and regu-
lating our perceptions. So that here, more than in
any other branch of human knowledge, we shall have
an opportunity of observm;^, how mjach an orderly
disposition of things tends to the ease and success of
our enquiries, by leaving us to canvass the parts sep-
arately, and thereby rise to a gradual conception of
the whole, without entangling ourselves with too ma-
ny considerations at once, in any single step of th©
investigation. For it will indeed be found, that a
dexterity and address, in the use of this last advan-
tage, serves to facilitate and- promote our discoveries,
almost beyond imagination or belief.
Sec. X. — The msihod of clas^ring our Percefiiions in
Arithmetic.
We have already explained the manner of reduc-
ing numbers into classes and of distinguishing these
passes by their several names. And now we are
farther to observe, that the present method of nota-
tion is so contrived, as exactly to fall in with this
form of numbering. For as in the nam.es of numbers,
v,-e rise from unita to iens^ from tens to hundreds, from
hundreds to thousands.) Isfc, so likewise in their nota-
tion, the same iigures, in different places, signify
E 2
226 DUNCAN'S ELEMENTS
the3e several combinations. Thus 2 in the first place^
on the rig;ht hand denotes two units^ in the second
place, it expresses so many tcnsj in the third hun-
clrrd-j in the fourth thousands. Ey this means it
happens, that when a number is written down in fig-
ures, as every figure in it expresses some distinct
combinaLion, and all combina.tions togetlier make up
the total sum ; so may the several figures be consid-
ered as the conskituent parts of the number. Thus
the number 2-136, is evidently, by the ver^/ notation,
distinguished into four parts, marked by the four fig-
ures that serve to express it. For the first denotes
?^o thousand, the second four hundred, the third ?/iz?*-
tij or three te?if>, and the fourth six-. These several
parts, though they here appear in a conjoined form,
may yet be also expressed separately thus, 2000, 400,
30, £md 6, and the amount is exactly the sam.e.
Sec. XI. — The heljis thence derived towards an easy
addition of niiuibers.
This then being the case, if it is required to find a
number equal to the sum of two ethers given ; our"
business is, to examine separately these given num-
bers, and if they appear too large and bulky to be
dealt with by a single effort of thought, then, since
the very notation, distir.guishes them into different
parts, Vv'c must content ourselves with considering the
parts asunder, and finding their sums one after an-.^
other. For since the whole is equal to all its parts,
if we find the sums of the several parts of which any
two numibers consist, we certainly find the total sum
of the tv/o numbers. And therefore, these different
sums, united and put together, according to the es-
tablished rules of notation will be the very num.ber
we are in quest of. Let it be proposed, for instance,
to find a number equal to the sum of tliese two':
OF LOGIC. 22/
2436, and 4552. As the finding of this by a single
f ffort of thought wouid be too violent an exercise for
the mind, I consider the figures, representing the-c
numbers, as the parts of whicii they consist, and
therefore set myself to discover their sums one after
I'nother. Thus 2, the first figure on the right hand
of the one, added to 6, the first figure on the right
hand of the other, makes 8, vrhich is therefore tiu;
sum of these two parts. Again, the sum bf 5 and 3,
the two figures or parts in the second place, is hke-
wise 8. But now as figures in the second place, de-
note not sirnrJe units, but tens ; hence it is plain,
that 5 and 3 here, signify five tens and three tens, or
50 and 30, whose sum therefore must be eight tens
or SO. And here again, 1 call to mind, that havmg
already obtained one figure of the sum, if I place
that now found immediately after it, it will thereby-
stand also in the second place, and so really express,
as it ought to do, eight tens, or SO. And thus it is
haopily contrived, that though in the addition of the
tens, I consider the figures composing ihem as denot-
ing only simple wiits, which makes the operation ea-
sier and less perplexed ; yet by the place their sum
obtains in the number found, it expresses the real
amount of the parts added, taken in their lull and
complete values. The same thing happens in sum-
ming the himdrecls and thousands ; that is, though
the figures expressing these combinxiticns, are added
together as simple units : yet their sums, standing
in'the third and fourth places of the num.ber found,
thereby really denote the hundreds and thousands,
and so' represent the true value of the parts added.
Sec. XU.—Cecmise hi the severaUteps by lohich it is
carried on,,the mind is put to little or no fatigue.
Hence then we have a manifest proof of the great
advantages derived irom :in ?.rtful method of classing.
22S DUNCAN^s ELEMENTS
o!jr perceptions. For as the numbers themselves are
by this means distinguished into different parts Vt'hich
brings them more readily within the compass of the
rtnderstancling ; so by taking these parts separatelvj
the operations about numbers are rendered very easy
and simple. And indeed it is particularly worthy our
notice, and though in adding two very large num.bers
together, the xvhole process is of sulTicient length ;
ye'j the several steps by which it is conducted, are
managed with incredible dispatch, and scarce any fa-
tigue to the mind. This is apparent in the example
given above, where we see, that in every advance from
one part to another, nothing more is required than
to add together the two figures in the like places of
tiie numbers to be summed. But what is yet more
wonderful, though in the progress of a long opera-
tion, the figures rise in their value as v/e advance,
and grov/ to signify thousands^ millions^ billions^ is'c^
yet so happily are they contrived for expressing the
different parts of numbers, that in every step of the
procedure w^e consider them as denoting only simple
units, ail other deficiencies being made up, by the
places their sums obtain in the total amount. And
thus it is so ordered in this admirable form of nota-
tion, that howqver large the numbers are that comp
under examination, they are nevertheless managed
v/ith the same ease as the most simple and obvious
collections ; because in the several operations about
them, the mind is neither tied down to the view of
too many parts at once, nor entangled with ?a7y con-
siderations regarding the bulk and composition of
those parts.
Sec. XIII. — This farther Illustrated by an Example in
MuUijilicaticjn.
And if these advantages are so very manifest in the
first and simplest rules of aritiimetic, much more da
OF LOGIC. 229
they discover themselves in these that are intricate
and complex. Let a man endeavour in his thoughts
to find the product of two numbers, each consisting
of twenty or thirty places, and that without consider-
ing- the parts separately ; I believe he will soon be
sensible, that it is a discovery far beyond the limits of
the human mind. But now in the progressive method
aboA-e explained, nothing is m.ore simple and easy.
For if we take the first figure on the right hand of the
one number, ar:d by it multiply every figure of the
other separately ; these several products, connected
according to the established iav^s of notation, must
truly represent the total product of this other, by that
part of the m.uitipiying num.ber. Let us suppose, for
instance, the figure in the unit's place of the muhijili-
er to be 2, and the three last places of the vndtip'd'
co.nd to be 432. Then, 2 multiplying 2 produces 4.,
which therefore is the fii'st part of the product. A-
g?.in, 2f multiplying 3 produces 6. But nov/ 3 stand-
ing in the second place of the multiplicand, denotes
its real value three ten-s^ or 30, v/hich therefore taken
tv>ice, amount to six tsna or 60. And accordingly
the figure 6, comJng after 4 ah'eady found, is thereby-
thrown into the second place of the product, and so
truly expresses 60, its full and adequate value. The
same thifig happens in multiplying 4, which standing
in the place qi hundreds^ its product by 2 is 800. —
But this very sum the figure 8, produced from 2 and
4, really denotes in the total product. Because com-
ing after 64, the two parts already found, it is thereby
determ.ined to the third place, where it of course ex-
presses so many hundreds. This process, it is evi-
dent, may be continued to any length we please ; and
it is remarlviable, that in like manner as in addition*
though the value of the figures in the multiplicand
continu?JIy rises up-on us, yet we all along proceed
233 DUNCAN'S ELE:vIENTS
with them as siinple units ; because the places of the
several products in the total amount, represent the
iust result ofmultiph-ing the figures. together, accorJ-
ifig to their true and adequate value.
Sec. XIV.— C/ the disposition of the several Products
in order toAdoition.
Having thus obtained the product by the first fig-
ure of tiie muiLiplier, we next take that in the second
place, and proceed v/ith it in the same manner. This
second operation gives us the effect of that figure,
considered as a simple digit. But as it stood in the
second place, and therefore really denoted so many
tens, hence it is plain, that the product now gained
must be yet multiplied hj ten^ in order to express the
true product sought. This is accordingly done in
the operation, by placing the first figure of this sec-
ond product under the second figure of the first pro-
duct. For this, when ihey come to be added togeth-
er, has the same effect as annexing a cypher, or mul-
tiplying by tcn^ as every one knows who is in the least
acquainted vrith the rules of arithmetic. In like man-
ner, when we multiply by the figure in the third,
place, as this new product is placed still one figure
backAvards, we do in effect annex two cyphers to it,
or multiply it by a hundred. And this we ought cer-
.tainiyto do; because having considered the multiply- -
ing figu-re as denocing only simple units, v.'hen it re-
ally expressed so many hundreds, the first operation
gives no more than the hundredth part of the true
product. The case is the same in multiplying by the
Iburth or fifth figures, because, the products still run-
ning backyrards^we thereby in effect annex as many
cyphers to them as bring them up severally to their
respective adoquate value. By this means it hap-
X^euij that thoii^^i the figures of the multiplier m eve-
ly advance, denote still higher and higher combina-
tions, yet vre rJl along proceed with them as simple
digits ; the disposition oi^ the several r-roducts in or-
der to addition making up for all the deficiencies that
arise from this Avay of considering them. When in
this method of procedure, v/e have obtained the pro-
duct of the multiplicand into all the different parts of
the m.ultiplier, by adding these products together Ave
obtain also the total product of the tv/o num.bers.^ — .
For since the whole is equal to ai\ its parts, nothing
is more evident, than that the product of any one
number into another, must be equal to its product in-
to all the parts of that ether : and therefore the sev-
eral partial products united into one sum, cannot but
truly represent the real product sought.
Sec. XV. — .AiimnietLcal cjierations^by behig carried on
171 a Progressive method^ rendered ecay and intelligible.
Thus Ave sec, that in questions of multiplication,
though the whole process is sometimes sufriciently
long and tedious, yet the several steps by v/hich it is
carried en are all very level to the powers of the un-
derstanding. For from the account given above it ap-
pears, that nothing more is required in any of them
than barely to multiply one digit by another. But
no'-v this easy rule of operation is wholly derived from
the before mentioned p.ddress in classing our percep-
tions. For to this it is owing, that the numbers un-
der consideration are distinguished into parts, and-
that the several parts are also clearly represented to
the mind in the very form of notation. Now as these
parts have an invariable relation one to ano'her, and
advance in their value by an uniform law of progres-
sior. ; the understanding by means of such a lii k can
easily hold them together, and carry its viev/s from
stage to stage T/itl:ciU perplexity or confusion; —
232 DUNCAN'S ELEMENTS
Hence it happens, that however large and mig-hty-
the numbers are, so far as to exceed the immediate
c^rasp of the mind ; yet by running gradually through
the several combinations of which they are made up,
v.e at leneth comprehend them in their full extent.
And because it vrould be impossible for the under-
standing to multiply' very large numbers one into an-
other, by a sirapie effort of thought ; therefore here
also it considers tlie_ parts separately, and, taking
them in an orderly series, advances by a variety of
successive steps, 'it is true indeed, in the progress
of the operation, the several figures rise in their val-
ue : but this consideration enters not the v/ork itself.
For there, as we have alrea.dy seen, though the char-
acters are taken as denoting only sirapie units, yet the
order and disposition of the partial products, exhibits
each according to its real amount. Hence in every
step, we have'only to multiply one digit by another,
v/luch as it is attended with scarce any difiiculty, the
whole process is carried on with wondrous dispatch.
And thus by a'series of easy operations, we at length
rise to discoveries, which in any other method of
procedure, vrould have been found altogether beyond
the reach of the mind.
Sec. XVI. The art of Classing our Perce fitiorm the
great Mean and Instrument rj Invention.
Since therefore bv a due and orderly disposition of
x:ur ideas, we can bring the most wide and extended
obiects upon a level with the powers of the under-
standing : and since by this also we abridge the fa-
tigue and labour of the m.ind, and enable it to carry
on its researches in a progressive method, without
which contrivance, almost ail the more remote and
distant truths of the sciences must have lain forever
■d fi-om our knowledge ; I think we may ventui-fe
OF LOGIC. 23S
to affirm, that the art of regulating and classhig our
perceptions is the great mean and instrument of in-
vention. It is for this reason that I have endeavour-
ed in so particular a manner to illustrate it from ex-
amples in numbers ; because v/e have here not only
a perfect model of the art itself, but see also in the
clearest manner, v/hat helps it furnishes towards a
ready comprehension of objects, and a masterly inves-
tigation of truth. Nor let any one find fault, as if v.'c
had insisted rather too long upon matters that are
obvious and knov/n to all. For I am apt to think,
that though very few are strangers to the received
method of notation, and the common rules of opera-
tion in arithmetic ; yet it is not every one that sets
himself to consider the address and sagacity that may
be seen in the contrivance of them, or to unravel
those principles of investigation, v.^hich we have here
so clearly deduced from them. And this I take to
be the reason, that v,^e sometimes meet with instanc-
es of men, who though thorougly versed in the art of
invention ; with regard to some particular branches
of knowledge ; yet if taken outof their usual track,
find themselves immediately at a stand, as if wholly
bereft of genius and penetration. With such men
invention is a mere habit, carried on in a manner
purely mechanical, without any knowledge of the
grounds and reasons upon which the several rules of
investigation are founded. Hence they are unfur-
nished Avith those general observations, which may
be alike usefully applied in all sciences, with only
some little necessary variations, suiied to the nature
of the subject we are upon. And indeed I know of
no surer way to arrive at a fruitful and ready inven-
tion, than by attending carefully to the procedure of
our own minds, in the exercise of this distinguished
faculty ; because from the particular rules relating
F 2
234 DUNCAN'S ELEMENTS
to any one branch, we are often enabled to derive
such general remarks, as tend to lay open the very
foundation and principles of the art itself.
Sec. XVII. — 27/-? manner of proceeding in the resoiu-
tion of Algebraic questions.
If now we turn our thoughts from arithmetic to al-
gebra^ here also we shall hnd, that the great inven-
tion lies, in so regulating and disposing our notices
of things, that v/e may be enabled to proceed grad-
ually in the search of truth. For it is the prin-
cipal aim of this science, by exhibiting the several
relations of things in a kind of symbolical language,
so to represent them to the imagination, as that
we may carry our attention from one to another, in
any order we please. Hence, however numerous
those relations are, yet by taking only such a num-
ber of them into consideration at once, as is suited
to the reach and capacity of the understanding, we
avoid perplexity and confusion in our researches, and
never put our faculties too much upon the stretch,
so as to loose ourselves amidst the multiplicity of
our own thoughts. As therefore in arithmetic^ we
rise to a just conception of the greatest numbers as
considering them made up of various progressive
combinations ; so likewise in algebra^ those manifold
Telations that often intervene, between known and un-
known quantities, are clearly represented to the mind,
by throwing them into a series of distinct equations.
And as the most difficult questions relating to num-
bers are managed "'vith ease ; because Ave can take
the parts or figures separately, and proceed with
them oi:e after another ; so also the most intricate
problems of algebra are in like manner readily un-
folded, by examining the several equations apart, and
unravelling them according to certain established
OF LOGIC. 235
rules of operation. And here it is well worth our
notice, that in very complicated problems, producing
a great number of different equations, it for the most
part so happens, that every one of them includes a
variety of unknown quantities. When therefore we
come to solve them separately, as it would too much
distract and entangle the mind, to engage in the pur-
suit of so many diflerent objects at once ; our first
business is, by artfully coupling the several equations
together, or by the various ways of multiplication,
subtraction, addition, and substitution, to derive oth-
ers from them more simple, until at length by such
a gradual process vre arrive at some new equation,
with only one unknovrn quantity. This done, we set
ourselves to consider the equation last found, and hav-
ing now to do with an object suited to the strength
and capacity of the mind, easily by the established
rules of the art, discover the- quantity sought. In
this manner Vv-e proceed with all the several unknown
quantities one after another, and having by a series
of distinct operations traced them separately, the ques-
tion is thereby completely resolved.
Sec. XVIII. — Of those other Artl/ices ivhich may be
considered as Subsidiary helps to Invention.
Hence it appears, that the business of invention, as
practised in algebra, depends entirely upon the art
of abridging our thoughts, reducing the number of
particulars taken under consideration at once to the
fewest possible, and establishing that progressive
method of investigation, which we have already so
fully explained from examples in arithmetic. I might
easily show that the same observation holds equally
in other sciences ; but having already exceeded the
bounds I at first prescribed to myself in this chapter,
shall only add, that besides the grand instruments of
236 DUNCAN'S ELEMENTS'
knowledge already mentioried, there are innumerable >
other aniiices, arising out of the particular nature of
the subiect we are upon, and which may be considered
as subsidiary helps to invention. Thus in geometry,
TTiany demonstrations cf problem.s and theorems are
wholly derived from the construction oi" the figure
made use of, and the drav/ing of lines from one point
to another. In like manner in algebra, the devising
of proper equations from the conditions of the ques-
tion proposed, and contriving neat expressions for
the unknown quantities, contiibute not a little to the
easy solution of problems. And when vv'e have even
carried on the investigation to some single equation
with only one unknovrn quantity ; as that unknown
(juantity may be variously perplexed and entangled
with others that are known, so as to require a multi-
plicity of different operations, before it can be disen-
gaged, which often involves us in ion.g and intricate
calculations, and brines surds and irrational quanti-
ties in our v/ay ; algebraists, to prevent in some
measure these inconvenientes, and shorten as much
as possible, the process, have faiien upon several
methods of substitution, Vv-hich are of great service in
very complicaied questions. But these and such
like artifices of invention, cannot be explained at
length in this short essay. It is enough to have giv-
en the reader a hint of them, and put him in the way
of unraveUing them himself, when he comes to apply
his thoi'gbts to those particular branches of knowl-
edge where they are severally made use of.
Sec. XiX.~0/ the great advantages arising from a
hapjiy Notation or expression of (jur Thov.ghis.
There is one thing however, that in a particular
manner deserves to betaken notice of, before we dis-
miss this subject j and that is the great advantages
OF LOGIC. 237
that ir.ay redound to science, by a happy notation or
expression of our thoughts. It is owing entirely to
this, and the method of denoting the several combi-
nations of numbers by figures standing in dilterent
places, tiiat the most complicated operations in arith-
metic are managed with so much ease and dispatch.
Nor is it less apparent, that the discoveries made by
algebra, are wholly to be imputed to that symbolical
language m.ade use of in it. For by this means we
are enabled to represent the relations of things in the
form of equations, and by variously proceeding with
these equations, to trace out, step by step, the several
particulars we are in quest of. Add to all this, that
by such a notation, the eyes and imagination are al-
so made subservient to the discovery of truth. For
the thoughts of the mind rise up and disappear, ac-
cordhig as ^YQ set ourselves to call them into view ;
and therefore, without any particular method of fixing
and ascertaining them as they occur, the retrieving
them agahi when out of sight, Vvould often be no less
painful than the very nrst exercise cf deducing them^
one from another. When therefore in the pursuit of
truth we carry our attention forward from one part
of the investigation to another, as nevertheless we
have frequent occasions to look back upon the dis-
coveries a.lready passed through, could these be no
otherwise brought into view, than by the same course
of thinking in which they were first traced, so many
different attentions at once must needs greatly dis-
tract the mind, and be attended with infinite trouble
and fatigue. But now, the method of fixing and as-
certaining our thoughts by a happy and well-chosen
notation, entirely ren^oves all these obstacles. For
thus, when we have occasion to run to any former
discoveries, as care is taken all along to delineate
them m proper characters, vfe need only cast our eye
238 DUNCAN'S ELEMENTS
upon that part of the process where they stand ex-
pressed, which will lay them at once open to the
mind, in their true and genuine form. By this means
we can at any time take a quick and ready survey of
our progress, and running over the several conclu-
sions already gained, see more distinctly what helps
they furnish towards the obtaining of these others we
are still in pursuit of. Nay further, as the amount
of every step of the investigation lies fairly before us,
by comparing them variously among themselves, and
adjusting them one to another, we come at length to
discern the result of th« whole, and are enabled to
form our several discoveries into an uniform and
Avell connected system of truths, which is the great
end and aim of all our enquiries.
Sec. XX. — Recajiitidation.
Upon the whole then it appears, that in order to
proceed successively in the exercise of invention, we
must endeavour as much as possible to enlarge tlie
capacity of the mind, by accustomiiig it to wide and
comprehensive views of things : that we m^ust habit-
uate ourselves to a strong and unshaken attention,
wdiich carefully distinguishes all the circumstances
tliat come in our way, and lets nothing material slip
its notice : in fine, that we must furnish ourselves
with an ample variety of intermediate ideas, and be
much in the exercise of singling them out and apply-
ing them for the discovery of truth. These prepar-
atory qualifications obtained, whcit depends upon art
lies chiefly in the manner of combining our percep-
tions, and classing them together with address, so as
to establish a progressive method of investigation. —
And here it is of great importance to contrive a prop-
er notation or expression of our thoughts, such as may
exhibit them ?>ccording to their real appearance in
OF LOGIC. 239
the mindj and distinctly represent their several divi-
sions, classes, and relations. This is clearly seen in
the manner of computing by figures in arithmetic,
but more particularly in that symbolical language,
which hath been hitherto so successively applied in
unravelling of algebraical problems. Thus furnish-
ed, we m.ay at any time set about the investigation of
truth ; and if we take care to note down the several
steps of the process, as the mind advances from one
discovery to another, such an arrangement or dispo-
sition of our thoughts constitutes what is called the
juethod of invention. For thtis it is plain that we fol-
low the natural procedure of the understanding, and
make the truths v. e have unravelled to succeed one
another, according to the order in which they present
themselves to the mJnd, while employed in tracing
and finding them out. And here again it well deserves
our notice, that as bv this means the whole investis:a-
tion lies distinctly before us ; so by comparing the
several steps of it among themselves, and observing
the relation they bear one to another, we are enabled
to form our discoveries into a regular system of
knowledge, where the truths advanced are duly link-
ed together, and deduced in an orderly series from
first principles. This other manner of combining our
thoughts, is distinguished by the name of the method
of science, which therefore now offers itself to be ex-
plained, and is accordingly the subject of the ensuing
chapter.
240 DUNCAN'S ELEMENTS
CHAP. II.
OF THE METHOD OF SCIENCE.
J^ec. I. — Knoivledge as derived from the contemfilaUon
of our idsas^ of a necessary and unchangeable nature ;
In order to give the juster idea of the rules peculiar
to this species of method, and establish them upon
their proper foundation, it will be necessary to begin
v/ith settling the meaning of the word science^ and
showing to what parts of human knowledge that term
may be most fitly applied. We have already observ-
ed, in the first chapter of the second book, that there
Ere three several ways of coming at the knov.iedge of
truth. First, by contemplaiing the ideas in our ov/n
minds. Secondly, by the information of the senses.
Thirdly, by the testimony of others. When we set
ourselves to consider the ideas in our own minds, we
variously compare them together, in order to judge of
their agreement or disagreement. Now as all the
truths deduced in this way, flow from certain connex-
ions and relations, discerned between the ideas them-
selves ; and as when the same ideas are brought into
comparison, the same relations must ever and invaria-
bly subsist between them ; hence it is plain, that the
knowledge acquired by the contemplation of our ideas,
is of a necessary and unchangeable nature. But
farther, as the relations between our ideas, are not
only supposed to be real in themselves, but also to be
seen and discerned by the mind ; and as when we
clearly perceive a connexion or repugnance between
any two ideas, we cannot avoid judging them to agree
or disagree accordingly ; it evidently follows, that our
knowledge of this kind is attended with absolute cer-
tainty and conviction, insomuch, that it is impossible
t:4i
for us to withhold our assent, or eiitertain any dt-ubt as
to the reality of truths so offered to the understand-
ing. The relation of equality between the whole and
all its parts, is apparent to every one who has formed
to himself a distinct notion of v.hat the words whrAs
and/tcr-i stand for. 2\ o man, therefore, v/ho has these
two ideas in his mind, can possibly doubt of the truth
of this proposition, that the whrjleis equal to ailits parts.
For this would only be ende?.vouring to persuade him-
self, that that was net, whif:h he plainly and unavoid-
ably perceives to be. So that in all cases, where v.e
disceni a relation between any of our ideas, whether
immediately by comparir g the one with another, cr
by means of intermedia': - ideas, that lay it open dis-
tinctly to the understar.ding ; the knowledge thence
arising is certain and I' ifitllibie. I say infallible ; be-
cause we not only percf jive and awT\ the truth of propo-
sitions so onered to tir.e mind, but, having at the same
time a clear view of the ground on which our assent
rests, are entirely satisfied within ourselves, that we
cannot possibly be deceived in this perception.
Sec. II. 'is f oioing from the inforwation of the senses,
begets imd'jubted assurance'^ but excludes not all pos-
sibility of being deceived ;
This second way of coming at knowledge, is by the
mean? of the senses. From them we receive infor-
matj'on of the existence of objects without us, of the
^^^ron and conjunction of different qualities in the same
s' object, and of the operations of bodies one upon
'another. Thus our eyes tell us, that there is in the
universe such a body as we call the sun, our sight and
touch, that light and heat, or at least tlie power of ex-
citing those perceptions in us, co-exist in that body ;
and lastly, by the same sight we also learn, that tire
has the power of dissolving metals, or of reducing
G 2
242 / DUNXAN's ELEMENTS
Tv'ood to charcoal and ashes. But now with regard
to this kind of knov/ledge v,e are to observe, that
though when the organs of the body are rightly dis-
posed, and operate in a natural way, v/e never doubt
the testimony of our senses, but from most of the
schemes of life upon their information : yet are not
the truths of this class attended with that absolute and
infallible assurance, which belongs to those derived
from the contemplation of our own ideas. We find
that the senses frequently represent objects as really
<ixisting, which yet have no being but in our own im-
aginations ; as in dreams, phrensies, and the deliri-
ums of a fever. A disorder too in the organs, makes
us ofcen ascribe qualities to bodies, entirely different
from those they appear to possess at other times.
Thus a man in the jaundice shall fancy every object
presented to him yellow ; and in bodily distempers,
v/here the taste is greatly vitiated, what naturally pro-
duces the idea of sweetness, is sometimes attended
Avith a quite contrary sensation. It is true, these ir-
regularities neither ought, nor indeed do they, with
considerate men, in any ways tend, to discredit the
testimony of experience. He that, awake, and in his
senses, and satisiied that his organs operated duly,
should take it into his head to doubt vrhether fire
would burn, or arsenic poison him, and therefore rash-
ly venture upon these objects, would soon be convinc-
ed of his error, in a way not much to his liking. As
nevertheless the senses do sometimes impose upon
us, there is no absolute and infallible security tha\
they may not at others ; therefore the assurance they
produce, though reasonable, satisfying, and sufficient-
ly well founded to determine us in the several actions
and occurrences of life, is yet of such a nature, as not
necessarily to exclude all possibility of being deceiv-
c:l. Hence some men go so far as to maintaittj that
OF LOGIC. 243
we ought to distrust our senses altogether ; nay,
Avhole sects among the ancients, because of this bare
possibility,' which really extends no farther than to
matters of experience and tesliiyicinj^ yet established it
as a principle, that we ought to doubt of every thing.
Nor are there wanting philosophers among the mod-
erns, who, upon the same grounds, deny the exist-
ence of bodies, and ascribe the perceptions excited
in us, not to the action of external matter, but to cer-
tain established laws in nature, which operate upon
us in such manner as to produce all those several ef-
fects that seem to flow from the real presence of ob-
jects variously effecting our perception. It is net
my design here to enter into a particular discussion
of these matters : all I aim at, is to show, that the
testimony of the senses, though sufficient to convince
sober and reasonable men, yet does not so unavoida-
bly extort our assent, as to leave no rooin for suspi-
cion or distrust.
Sec. III. — As founded ufion testbnony^ is of a still more
certain nature^ though in Tncinij cases embraced with-^
out vjavering or distrust.
The third and last way of coming at truth is hj
tlie report and testimony of others. This regards
chiefly past facts and transactions, which having no
longer any existence, cannot be brought within the
present sphere of our observation. For as these
could never have fallen under cur cognizance, but by
the relations of such as had sufficient opportunities
of being informed ; it is hence apparent, that all our
knov.iedge of this kind is wholly founded upon the
conveyance of testimony. But now, although this in
many cases is a sufficient ground of assent, so as to
produce a ready belief in the mind, yet is it liable to
still greater objections than even the reports of expe*
244 B'tTNCAN's ELEMENTS ^
rierxe. Our senses, it is triie^ on some occasions de-
ceive us, and therefore they may possibly on others.
But this bare possibility creates little or no distrust ;
because there are fixed rules of judging-, M-hen they
operate according to nature, and when they are pre-
Yented or given up to caprice. It is otherwise in
matters of mere human testimony. For there, be-
sides the supposition that the persons themselves may
have been deceived, there is a farther possibility, that
they may have conspired to impose upon others by a
false relation. This consideration has the greater
weight, as we frequently meet v/ith such instances of
disingenuity am.cng men, and know it to be their in-
terest in some particular cases, to dissemble and mis-
represent the truth. It would, nevertheless, be the
height of folly, to reject all human testimony without
distinction because of this bare possibility. Who can
doubt whether there ever v\^ere in the world such con-
querors 3.2 Alexander and Julius Casar ? There is no
absolute contradiction, indeed, in supposing, that his-
torians may have conspired to deceive us. But such
an universal concurrence to a falsehood, without one
contradicting voice, is so extremely improbable, and
so very unlike what usually happens in the world,
that a wise man could as soon persuade himself to
believe the grossest absurdity, as to admit of a sup-
position so remote from every appearance of truth,
i-ience the facts of histoiy, when v/ell attested, are
readily embraced by the m.ind ; and though the evi-
dence attending them be not such as produces a ne-
cessary and infallible assurance, it is yet abundantly
sufficient to justify our belief, and leave those without
excvise, who upon' the bare ground of possibility, are
lor rejecting entirely t];e conveyance of testimony.
OF LOGIC. 245
Sec. IV. — Science belongs entirely to that branch of
kno%vledy;e nvhich is derived from th^ contemplation
of Gur Ideas.
Upon the -whole, then, it appears, that absolute cer-
tainty, such as is attended with unavoidable assent,
and exchides all possibility of being deceived, is to be
found only in the contemplation of our own ideas. In.
matters of experience and testimony, men, we see>'
may fi^ame pretences lor suspicion and distrust : but
in that part of knowledge which regards the relations
of our ideas, none such can have place. For as all
these several relations are either immediately dis-
cerned by the mind, or traced by means of immedi-
ate ideas, where self-evidence is supposed to acccm.-
pany every step of the procedure, it is absolutely im-
possible for a man to persuade him.self that that is
not, which he plainly and necessarily perceives to be.
Now it is to knovv'ledge, attended with this last kind
of evidence alone, that in strictness and propi^iety of
speech we attribute the na.me of science. For science
implies perception and discernment, vrhat we our-
selves see and cannot avoid seeing ; and therefore
"has place only in matters of absolute certainty, where
th€: truths advanced are either intuitive propositions,
or deduced from them in a way of strict demonstra-
tir;n. And as this kind of certainty is no where to be
forjnd, but in investigating the relations of our ideas ;
hence it is plain, that science^ properly speaking, re-
gards v/holly the first branch of human knowledge ;
tjiat i-vhich \\& have said is derived from a contempla-
tion of the ideas in our own minds.
Sec. V,> — Our Knowledge of the real Existence of Ob"
jects not Intuitive.
But here I expect it will be asked, if science and
dcmonstraPio?! belong only to the ccnsideration of cur
246 DUNCAN'S ELEMENTS
own ideas, what kind of knowledge it is, that we hare
relatin:^ to bodies, their powers, properties, and oper-
ations one upon another ? To this I answer, that we
have ah^ady distinguished it by the name of natural
or exfierimental. But that we may see more distinct-
ly v/herein the difference between scientifical and
7?arzo'<7/ knowledge lies, it may not be improper to add
the following observations. When we cast our eyes
towards the sun, we immediately conclude, that there
exists an object v/ithoutus, corresponding to the idea
in our minds. We are, however, to take notice, that
this conclusion does not arise from any necessary and
unavoidable connexion discerned, between the ap-
pearance of the idea in the mind, and the real exist-
ence of the object without us. We all know by ex-
perience, that ideas may be excited, and that too by
a seeming operation of objects upon our senses, vrhen
there are in fact no such objects existing ; as in
dreams, and the deliriums of a fever. Upon what
then is the before-mentioned conclusion properly
grounded ? Why, evidently upon this : that as we
are satistie 1 our organs operate duly, and know that
every effect must have a cause, nothmg is more nat-
ural than to suppose, that where an idea is excited
in the mind, some object exists corresponding to the
idea, v/hich is the cause of that appearance. But as
this conclusion, by what we have seen, is not neces-
sary and unavoidable, hence there is no intidihn in
the case, but merely a probable conjecture, or reason-
able presumption, grounded upon an intuitive truth.
Sec. VI.- — ibsolute Certainty in natural KnoTolecige con-^
Jined to what falls under our ivmediate notice.
Again, when a piece of gold is dissolved in aqua
rcgia^ we see indeed and own the effect produced,
but cannot be said, in strictness and propriety of
OF LOGIC. 247
speech, to have any perception or discernment of it.
The reason is, because being- unacquainted vrith the
intimate nature both of aqua rcgia and gold, we can-
not, from the ideas of them in our minds, deduce
why the one operates upon the other in that particu-
lar manner. Hence it is, that our knov.iedge of the
facts and operations of nature extends not with cer-
tainty beyond the present instance, or what falls un-
der our imm.ediate notice ; so that in all our research-
es relating to them, we must proceed in the way of
trial and experiment, there being here no general or
universal trutlis, whereon to found scientijical deduc-
tions. Be::ause the solution of gold in aqua regia
hol9s in one experiment, v/e cannot thence infallibly
conclude that it will hold in another. For not know-
ing upon \y:hat it is, in either of these bodies, that the
effect here mentioned depends, v/e have no absolute
certainty in any new experiment we propose to make,
that the objects to be applied one to another have that
precise texture and constitution from which this solu-
tion results. Chemists, knov/ by experience, that bod-
ies which go by the same name, and have the same
outward appearance, are not ahvays, Iiowever, exact-
ly alike in their pov/ers and operations. In vain do
they often search for those properties in one piece of
antimony^ which, on former occasions, they may have
found in another ; and by this means, to their no small
iTiortification, find themselves frequently disappoint-
ed, in very costly and promising experiments. Nor
have we any express and positive assurance, that the
very bodies with which we have formerly made exper-
iments, continue so exactly the same, as to afford the
like appearances in any succeeding trial. A thousand
changes happen every moment in the natural v/orld,
v/ithout our having the least knowledge or perception
of them. An alteration in cur atmosphere, the ap-
248 DUNCAN'S ELEMENTS
proach or recess of the sun, his declination towards
the north or south, not only vary the outward face of
things, but occasion manyxhanges in the human con-
stitution itself, which we yet perceive nor when they
happen ; nor should ever be sensible of, but by the
effects and consequences resulting- from them. And
whether alterations analogous to these may not some-
times be produced in the frame and texture of many
bodies that surround us, is what we cannot with cer-
tainty determine. Hence, from an experiment's suc-
ceeding in one insta.nce, we cannot infallibly argue,
that it will succeed in another, even with the same
body. The thing may indeed be probable, and that
in the highest degree ; but as there is still a possibil-
ity that some change may have happened to the body,
unknown to us, there can be no absolute certainty
in the case.
Sec. VIL — W/iat kind of Knowledge of Body ivoidd
deserve the name of Science,
Had we such an intimate acquaintance with the
structure both of aqua rcgia and gold, as to be able
thence to discern why the one so operates upon the
other as to occasion its dissolution ; insomuch that
from the ideas of them in our own minds, we could
clearly deduce, that bodies of such a make applied
one to another, must necessarily produce the effect
here mentioned ; our knoy*^ledge v/ould then be sci^
endfcal^ and stand upon the foundation either of intu-
ition or de7nonstration, according as the perception was
immediate, or attained by means of intervening ideas.
In this case, therefore, having two standard ideas in
our minds, whose relations we perfectly v^^ell know ;
^.vherever we found objects conformable to these ideas,
v/e could then pronounce with certainty, that the ap-
plication of them oiie to another would be attended
OF LOGIC= 249
with the above effect : because, whatever is true in
idea, is unavoidably so also in reality cf thirigs> v/here
things exist answerable to these ideas. If it be tnje
in idea, that a parelleiogram is the double cf a tiian'^le,
standing upon the same base, and bet'vveen the same
parellels ; the same will be trac of every real trian-
gle and parelleiogram, that exist with the conditions
here mentioned. We are likewise to observe, that
the changes to which bodies are daily liable, could
produce no confusion or perplexity in natural kncv.l-
edge, did it stand upon the foundation here mention-
ed. For in such a case, the pov/ers and properties of
objects being deduced from the ideas of them in cur
o^vn minds, would no otherv.ise be applied to things
really existing, than as these things are found perfect-
ly conformable to our ideas. When, therefore, an
alteration happened in any body, as it vvould by tiiis
means differ from that standard idea v.hence its form-
er properties were seen to flow, we must of course
be sensible, that some suitable change would fellow
in the properties themselves, and that its powers and
operations, in regard of other bodies, would net be in
all respects the same.
Sec. VIII. — Exfierience the ordy foimdatlon of Natur-
al Knowledge.
But what is still more remarkable, we should, up-
on this supposition, be able to determine the mutual
action arid influence of bodies, without having re-
course to trial or experiment. Had w^e, for instance,
a perfect knowledge of the intimate nature and com-
position of an animal body, arxd of that particular
poisoji that is infused into it by the bite of a viper, so
as clearly and distinctly to discern how they are adapt-
ed one to another ; we might thence scitntiflcally de-
duce, vrithout the helo of experiments, tliat the bite
H 2
250 DUNCAN'S ELEMENTS
o^ a viper would so unliinge the hiiniaD fabric, and
produce such ferments and coinbustioDs in it, as must
necessarily be followed by a total extinction of a!! the
vital functions, and leave that admirable machine a
iiiere lifeless lump. But as such perfect and ade-
cjuate ideas of objects, and their mutual habtiudes
one to another, are plainly beyond the reach of our
present faculties ; it were vain for us to think of im-
proving natural knowledge by abstract reasoning or
Ecientitical deductiojis. Experience is here the true
and proper foundation of our judgments, nor can we
by any other means arrive at a discovery of the sev-
eral powers and properties of bodies. How long
might a man contemplate the nature of hemlock,
examine the structure of its parts in a microscope,
and torture and analyse it by all the processes of
chemistry, before he could pronounce with certainty
the exTect it will have upon a hum.an body ? One sin-
gle experiment lays that open in an instant, v/hich
ail the vrit and invention of men would never of them-
selves have been able to trace. The same holds in
all the other parts of natural philosophy. Our dis-
coveries relating to electricity, the powers and prop-
erties of the load-stone, the force of gun-powder, Sec.
were not gained by reasoning, or tlie consideration of
cur abstract ideas, but by means of experiments made
with the bodies themselves. Hence it happened, that
while the philosophy of Aristotle prevailed in the
schools, v/hich dealt much in metaphysical notions,
occult qualities, sympathies, antipathies, and such like
words without meaning ; the knov/ledge of nature
was at a stand : because m.en pretended to argue ab-
stractedly about' the tilings of which they had no per-
fect and adequate ideas, whereon to ground such a
method of reasoning. But now in the present age,
that we have returned to the way of tri?d and experi-
OF LOGIC. zsl
•Rient, which is indeed the only true foundation of nat =
ural philosophy ; great advances have already been
made, and the prospect of still greater lies before us.
Sec. IX. — Di^erence beiween Scierdifical cjid JVatural
KncTjlsdgc.
And thus at length vre may sufficiently understand
wherein the proper difrerence lies, between scientiP-
cal and natural knowledge. In matters of science
v.e argue from the ideas in our ovvii minds, and the
connexions and relations they have one to another.
And as v.hen these relations are set clearly and plain-
ly before us, we cannot avoid perceiving and owning
them, hence all the truths of this class produce ab-
solute certainty in the mind, and are attended with
a necessary and unavoidable assent. It is otherwise
in the case of natural knowledge. Intuition and in-
v.-ard perception have here no place. We discern
not the powers and properties of those objects that
surround us, by any view and comparison of the ideas
of tficm one v/ith another, but m.er^Iy by experience,
and th.e impressions they make on the senses. But
now the reports of sense happening in some instanc- •
es to deceive us, we have no infallible assurance that
they may not in others ; which weakens not a little
tiie evidence attending this kind of knowledge, and
leaves room for suspicion and distrust. Nay, what
is yet more considerable, as we have no perfect and
adequate ideas of bodies, representing their invvard
constitution, or laying open the foundation upon which
their quaiicies depend, Vv'e can form no universal pro-
positions about themi, applicable with certainty in all
particular instances, i ire, we say, dissolves metals.
This, though expressed indefinitely, is, however, only
a particular truth, nor can be extended with absolute
assurance, beyond the several trials made. The rea-
252 DUNCAN'S ELEMENTS
COD is, that being ignorant of the inward frame and
coixiposition both of fire and metals ; when objects
are ofiered to us under that name, \ve ha.ve therefore
no positive certainty that thev are of the very make
and texture, requisite to the success of the experi-
ment. The thing may indeed be probable in the
highest degree ; but for v.ant of standard and settled
ideas, we can never arrive at a clear and absolute per-
ception in the case.
Sec. X. — The manner of Ecasonin_^ in J',a.tural Kncirl-
ed^'p.
As nevertheless, it is certain that many general
conclusions in natural philosophy are embraced \\\t\\-
out doubt or hesitation ; nav, that we form most of
the schemes and pursuits of life upon that founda-
tion ; it will naturally be asked here, how come we
by this assurance ? I answer, not scientifically, and
in the way of strict demonstration, but_by analogy,
and an induction of experiments. We distinguish
lire, for instance, by such of its qualities as lie more
immediately open to the notice of the senses ; am.ong
w\hich light and heat are the most considerable. Ex-
amining still farther into its nature, we find it like-
wise possessed of the power of dissolving metals.
But this new property not having any necessary con-
nexion that vre can trace, with those other qualities
by which fire is disthiguished, we cannot therefore
argue with certainty, tliat wherever light and heat,
&c. are, the power of dissolving m.etals co-exists with
them. 'Tis not till after we have tried the thing in
a variety of experiments, and found it ahvays to hold,
that we begin to presume there may be really some
such connexion, though our views are too short and
imperfect to discover it. Hence we are led to frame
H general conclusion, arguing from what has already
OF LOGIC. 253
happened, to what vrill happen again in the like cases,
insomuch that where we meet with all the ether prop-
erties of fire in any body, we have not the least doubt,^
but that upon trial, the power above mentioned will
be found to belong to it also. This is called reason-
ing by analogy ; and it is, as Vv'e see, founded entire-
ly upon induction, and experiments made with par-
ticular objects ; the m.ore precise and accurate our
ideas cf these objects are, and the greater the variety
of experiments upon vrhich we build our reasoning,
the more certain and undoubted v>iH the conclusions
be. 'Tis in this ms.nner we arrive at all the general
truths of natural knowledge : as that the bite of a cer-
tain ainmal is mortal ; that a needle touched by a
load-stone points to the north ; that gravity belongs
universally to ail bodies : and innumerable others,,
wliich, though not capable of strict demonstration,
are nevertheless as readily embraced upon the foun-
dation of analogy, as the most obvious and intuitive
judgmients ; nay, and become fixed and steady prin-
ciples of action, in all the aims and pursuits of life.
Sec. XI. — Hovj even S:i?nti/ical Rmsoriing 7nay be in-
iroduced into it.
And here again it is particularly remarkable, that
having ascertained the general properties of things by^
analogy, if we proceed next to establish these as/206-
tulata in philosophy, vre can, upon this foundation,,
build strict and mathematical demonstrations, and
thereby introduce scientifical reasoning into natural
knovviedge. In this m.anner, sir Isaac jYewtonhdiVm^
determined the laws of gavity by a varity of experi-
ments, and laying it down as a principle, that it op-
erates according to those laws through the whole
system of nature ; has thence, in a way cf strict de-
monstralioDj deduced the v.'hole theory of the heaven-
254 DUNCAN'S ELEMENTS
ly motions. For grantinfj once this /losfulatum, that
gravity belongs universally to all bodies, and that it
acts according to their solid content, decreasing vrith
the distance in a given ratio ; v/hat sir Isaac has de-
termined in regard to the planetary motions, foiiovvs
from the bare consideration of our own ideas ; that
is, necessu-rily and scient{ficalli>. Thus iikev.'ise in
ojnics^ if v/e lay it dov/n as a principle, that light is
f«ropagated on all sides in right lines, and that the
rays of it ar? reflected and refracted according to cer-
tain fixed invariable bj.vs all which is known to be
true by experience ; we can upon this foundation es-
tablish mathematically the theory of vision. The
same happens in mechanics^ hydrostatics^ pneumatics^
&:c. where from fiostulata ascertained by experience,
the whole theory relating to these branches of knovri-
edge follows in a v/ay of strict demonstration. And
tills I take to be the reason why many parts of na-
tural philosophy are honored with the name of scienc-
es. Not that they are ultimately founded upon in-
tuition ; but that the several principles peculiar to
them being assumed upon tlie foundation of expe-
rience, the theory deduced from these principles is
established by scicntlfical reasoning.
Sec. ^ll.—'Ytt still Ex/ierience is the ultimate Ground
of our Assent.
Could we indeed discern any necessary connexion
between gravity and the known essential qualities of
matter, insomuch that it was inseparable from the ve-
ry idea of it ; the whole theory of the planetary mo-
tions would therj be strictly and properly scitrdljical.
For seeing, from the notion of gravity, vve can de-
monstratively determine the laws that bodies will ob-
serve in tncir revolutions, in any known circumstanc-
es j if Uie Circumstances relating to any system of
OF LOGIC. 255
bodies can be traced, and gravity is sv.pposcd essen-
tial to tlieni, we can then, IVom the bare consideration
of our own ideas, deduce all their nicticns and phe-
nomena. Now this is precisely what sir Isaac has
done in regard to our planetary system. He has de-
termipicdthe circumstances of the bodies that com-
pose it, in respect of situation, distance, magnitude,
£^c. all which being supposed, if they are essentially
actuated by gravity, their several revolutions and ap-
pearances must be equally essential. But as the
principle of gravitation cannot be accounted for by the
known qualities of matter, neither can this theory be
immediately deduced from the idea of bcdy ; and
therefore, tho' our reasoning in tr.is part of philosophy
be truly scientihcai, yet as the prlrxipls upon which
that reasoning is grounded, is derived fi^om experi-
ence, the theory itself must needs ultimately rest up-
on the same foundation. And thus even the doctrine
cf the planetary motions, though seemingly establish-
ed by mathematical reasoning, falls yet, in strictness
and propriety of speech, under the head of natural
knowledge. For in this precisely consits the differ-
ence between science^ and what we call the philoso-
phy of nature ; that the one is grouTided ultimately
on iruuidon, the other on experience. As the obser-
vation here m.ade holds alike in all the ether branches
of natural philosophy, into which 5rz>«''//?rfi/ reasoning-
has been introduced ; it is hence apparent, that they
are not scieiicts, in the strict and proper sense of the
word, but only by a certain latitude of expresf.ion
common enough in all languages. What \yq have
therefore said above, relating to the impossibility of
improving natural knovrledge, by scientifical deduc-
tions, is not contradicted by any thing advanced in
this section. We there meant deductions grounded
Ultimately en intuition, and derived from a consider-
256 DUNCAN'S ELEMENTS
ation of the abstract ideas of objects in our own minds ;
liot such as flow from posiulaca^ assumed upon the
foundation of experience. For these last, as v.e have
ah-eady observed, are not truly and properly scientifi-
cal, but have obtained that name merely on account of
the way of reasoning in which they are collected from
the said posiulata.
Sec. XIII. The manner of Reasoning in Hisioricle
Knorjledge,
If then absolute and infallible certainty is not to be
obtained in natural knowledge, much less can we ex-
pect it in historicle. For here testimony is the only
rround of assent ; and therefore the possibility of our
being deceived, is still greater than in the case of ex-
perience. Not only he v^dio reports the fact may him-
self have formed a wrong judgment ; but could we
even p-et over this scruple, there is still room to sus-
pect, that he may aim at imposing upon us by a false
narration. In this case, therefore, it is plain, there
can be no intuition or inward perception of truth, no
strict and absolute dem.cnstration, and consequently
no science. There is, however, a way of reasoning
even here, that begets an entire acquiescence, and
leads us to embrace without wavering, the facts and
reports of history. If, for instance, it appears, that
the historian was a man of veracity ; if he was a com-
petent judge of v/hat he relates ; if he had sufficient
opportunities of beingjinformed ; if the book that bears
his name was really written by him ; if it had been
handed down to us uncorrupted ; in fine, if what he
relates is probable in itself, falls in naturally with the
other events of that age, and is attested by contempo-
rary writers ; by these and such like arguments,
founded partly on criticism., partly on probable conjec-
ture, wc iadge of past transac dons j and though they
OF. LOGIC. 257
are not •'!apablc oisci^ntifical proof, yet In manv cases
we arrive at an undoubted assurance of them. For
as it is absurd to demand mathematical demonstra-
tion in matters of fact, because they admit not of that
kind of evidence ; it is no less so to doubt of their
reality, when they are proved by the best arguments
their nature and quality v/ill bear.
Sec. XIV. — Sce/iticisms nececsarily erczludcdfrom mat-
ters of Science ;
And thus v/e see, in the several divisions of human
knovv ledge, both v/hat is the ground of judging, and
the manner of reasoning, peculiar to each. In sci^M-
tifical knowledge,, which regards wholly Iho abstract
ideas of the mind, and those relations and connexions
they haxe one vvith another ; our judgments are
grounded on intuitioji, and the manner of reasoning is
by clemo'/ist ration. In natural knowledge, res'>ectiiip-
objects that exist v/ithout us, their powers, properties,
and mutual operations ; we judge on the foundacion
of exjierience and reason by induction and analogy.
Lastly, in historical kaovjledge, which is chiefly con-
versant about past facts and transactions, testbnony is
the ground of judgment, and the way of reasoning is
by criticism ^t\A firobabls ccnjecturQ. And now I think
we are able effectually to overthrow that absurd kind
ot sce/iiicis7n maintained by some of the ancients v/hich
brings all propositions upon a level, and represents
them as equally uncertain. What gave the first rise
to this doctrine was, capi ice of certain philosonhei's,
who observing that the reports of sense and testimo-
ny v/ere in some instances deceitful, took thence oc-
casion to suppose that they might be so likewise in
others, and thereupon established it as a principle,
that we ought to doubt of every thing. But even with
respect to this doubtinor, we arc to observe, that it caa
12
258 DUNCAN'S
in Tizt extend no further, than to matters cf ex/ic
vie nee and testimony^ being totally and necessarily ex-
ckided from scientifccal knovv^ledge. When ideas
make their appearance in the understanding, it is im-
possible for us to doubt of their being there. And
vvhen the relations of any, of our ideas are clearly an^l
distinctly discerned by the mind, either immediate-
ly, which is intiiithr:^ or by m.cans of intervening
ideas, which is dtmonstradon ; it would be in vain for
us to endeavour to persuade ourselves that that is not,
which we plainly and unavoidably perceive to be.—
In this case, therefore, v/e cannot withhold our as-
sent ; trutii forces its way over all opposition, and
breaks in wiih so much light upon the mind, as to be-
get absolute and infallible certainty.
Sec. XV. dr.d to be admitted with caution inmatters
of experience and te8ti?noni/.
Indeed in natural and historical knowledge scepti-
cism m.ay have place ; because, as we have said, there
is a possibility of our being deceived. But then it is
to be observed, that a bare possibility is a very weak
o round whereon to bottom any philosophical tenet.
it is possible, that Great Britain may be swallowed
up by the sea before to-rnorrow ; but I believe no
man is on this account inclined to think it will be so.
It is possible the whole human race may be extin-
guished the next instant ; yet this possibility creates
no apprehension that the thhig itself will really hap-
pen. In a word, we ought to judge of tilings by the
proofs brought to support ihem, not by bare abstract
possibilities ; and v/hen we have all tlie evidence, they
are capable of, that alone is sufficient to convince,
tiiough perhaps the contrary cannot be shown to im-
ply a contradiction. Will any wise and considerate
man doubt V. hether tliere be such a place as Africa,
OF LOGIC 259
because we cannot prove, by any necessary argument,
that it is absolutely impossible ail tlie relations con-
cerning it should be false ? Strict and rigorous de-
monstrations belong not to history, or the philosophy
of nature. The way of reasoning, in these branches
of knowledge, is by arguments drawn from expe-
rience and testimony. And V, hen the truth of ?.ny
proposition is in this manner suiTiciently ascertained,
insomuch that it appears witli all the evidence it is
capable of, and we have as great reason to believe that
it is, as we could possibly have, supposing it were,
is not this upon the matter as satisfactory as demon-
stration ? It must be owned, indeed, there is no in-
v/ard perception in the case ; and tlierefore our assent
cannot be said to be necessary and unavoidable. —
Men may in thcise matters be 5rt^///;fcs, if they please ;
and if they are resolved upon it, it is in vain to con-
tend with obstinacy and preverseness. I cannot,
hovrever, but observe, that if they will really act up
to their own principles, and treat all things in good
earnest as uncertain, that admit not of strict scientifical
proof, their conduct must be the very madness of folly.
No man can demonstrate mathematically, that poison
has not been conveyed into his meat or drink. And
if he will be so very cautious as not to taste of either,
till he has reached this degree of certainty, I know
no other remedy for him, but that in great gravity
and wisdom he must die for fear of death. The truth
of it is, the most zealous patrons of scepticism^ after
ail their pretended doubts a.nd scruples, find it yet con-
venient to behave, in the several occurrences of life,
as if they gave entire credit to the reports of sense
and testimony. They will no more venture upon a
dose of arsenic, or rush into the midst of a glowing,
furnace, than if they verily believed death would be
the conseq^uence. And though in this it must be
260 DUNCAN'S ELEMENTS
ovrT.ed they act discreetly^ yet have we hence at the
same time a very convincing argument of the absur-
dity of those notions they affect to entertain. In re-
ality, can any thing be more ridiculous, than to give
into a scheme of thinking, which we iind ourselves
necessitated to contradict in almost every occurrence
of life ? Opinions are not to be taken up out of ca-
price' and fancy, but to serve as principles of action^
and standing rules of behaviour. When they answer
jxt this main purpose, they are unavailing and fruit-
less, and an obstinate adherence to them, in spite of
i-epeated admonitions of experience, justly deserves
to be branded fo? felly. We shall not, therefore, at-
tempt to multiply arguments in a matter so obvious,
it sufficiently ansvy^ering our present purpose to h?ive
shown, that doubting and uncertainty have no place
in scientiiicai knowledge, and that even in matters of
liistory, and the facts of nature, and undistinguisliing
^:cepticism would bi in the highest degree absurd.
Sec. XVI. — ■Siicnce applicable to the Concer7is of Hu-
man Life.
But here, perhaps, it will be asked. Why all this
mighty noise about science, when, even according to
the present account, it seems to be so very capricious
and arbitrary a thing t For seeing it is whcily confin-
ed to tlic consideration of our ideas, and we are at
iiherty to frame and combine those ideas at pleasure,
this indeed opens a v/ay to castles in the air, of cur
Gwu building, to many chimerical and fanciful S}s-
lems, v/hich 'm^Vi. of warm and lively imaginations
love to entertain themselves v-ith, but promises little
of that knowledge which is worth a wise mail's re-
gard, and respects the great ends and purposes of
\\i^. \V'here is the advantage of barely contemplat-^
mg our ideasj :uid ira':ing their several habitudes and
OF LOGIC. 261
relations, when it is in truth the reality of things that
we are chiefly concerned to know, and those respects
they bear to us and one another ? To this I answer :
that if indeed our ideas no v.ay regarded things them-
selves, the knowledge acquired by their means would
be of very little consequence to human life. But
since, as vre have already observed, Vvhatever is true
in idea, is unavoidably so also in the reality of things,
where things exist answerable to these ideas ; it is
apparent, that by copying our ideas with care from the
real objects of nature, and framing them in a ccn-
forr.iity to those conjunctures and circumstances in
v.hich vre are most likely to be concerned, a way is
laid open to discoveries of the greatest importance to
mankind. For in' this case, our several reasonings.
and conclusions, holding no less of the objects them-
selves, than of the ideas by v/hich they are represent-
ed, may be therefore applied v.'ith certainty to these
objects, as often as they fall under our notice. Thus
mathematicians, having formed to themselves ideas
of cones, cylinders, spheres, prisms. Sec. variously
compare them together, examine their several prop-
erties, and lay down rules by which to calculate their
relative bulk and dim.ensions. But nov^^ as bodies an-
swering in figure to these ideas come frequently un-
der our observation, we have by this means an oppor-
tunity of applying mathematical knowledge to the
common concerns of life ; and by determining pre-
cisely the quantity of extension in each body, can the
l^etter judge how far they will answer the purposes
we have in view. The same thing happens in poli-
tics and morality. If we form to ourselves ideas of
Luch communities, connexions, actions and conjunc-
tures, as do or may subsist am.ong mankind ; all our
reasonings and conclusions will then respect real life,
iUxd serve as steady maxims of behaviour in the sev-
262 DUNCAN'S ELEMENTS
€!*al circumstances to which it is liable. It is not,
therefore, enouc^h that we set about the considerdtion
of any ideas vl random ; we must further take care
that those ideas truly regard things themselves ; for
although knowledge is always certain, when derived
Irom the ccnteniplation of our own ideas, yet it is
then only useful .aid worthy our regard, vvhen it re-
spects ideas taken from the real objects of nature, and
strictly related to the concerns of human life.
Sec. XVII. — T/ic tru^thodof science begins ivith asctr-
tuining our Ideas ;
Having thus shov/n that there is such a thing as
science, fixed and ascertained the bounds of it, and
explained its great use and importance in the affairs
©f mankind ; it nov/ remains that we lay down the
rules of method peculiar to this branch of knov.iedge,
and give some account of the. manner in wliich that
certainty and conviction which are inseparable from
it, may be most naturally and effectaally produced^
8cic7ice^ as we have said, regards v.holly the abstract
ideas of the mind, and the relations they have one to
another. The great secret, therefore, of attaining it
lies in so managing aiid conducting our thoughts^ as
that these several relations may be laid open to the
view (A the understanding, and becoirie the necessa-
ry and imavoidable objects of our perception. In or-
der to this we must make it our first care, distinctly
to frame and settle the ideas about which our enqui-
ries are to be employed. For as the relations sub-
sisting between them can no otherwise be discerned,
than by comparing them one with another — and as
this comparison' necessa,rily supposes that the ideas
themselves are actually in the mind, and at that very
lime under car immediate inspection — it plainly foi-
law-s, tliat all science must begin with fixing and as-
OF LOGIC. Z63
cevtaining those ideas. Now cur ideas, as has been
ah^eady observed in the first book, come all very na-
turally within the division oi sir.ipJe ^^.wd co7nplex. —
Eim/ile ideas are excited by actual impressions made
-upon the understanding ; and as they exist under one
nniform appearance, v/ithout variety or composition,
are in no danger of being- mistaken, or confounded
one with another. It is otherwise in our complejc
conceptions. For these consisting of many simple
ideas joined together, great care must be taken, that
we acquaint ourselves with the true number combin-
-ed, and the order and manner of their connexion. — .
By this means alone are these our most intricate no-
tices, kept distinct and invariable, insomuch that in
all our several views cf them, they ever have the
■same appearance, and exhibit the sam.e habitudes and
respects. Here, therefore, properly speaking, the
art of knowledge begins. For although v/e find it ea-
sy enough to bound and settle our ideas, where they
consist of but few sirnpie perceptions ; yet v/hen they
grow to be very complicated, it often requires great
address and management to throw them into such
views as may prevent that confusion which is apt to
arise from the joint consideration of a multiplicity of
different objects Hence that gradation in the com-
postion of Gur ideas which we have explained at large
in the last chapter of the first book. For as they are
by this -means formed into diiTerent orders, and these
orders arise continually one out of another ; the un-
derstanding, by taking them in a just succession,
gradually mounts to tne highest conceptions, and can,
at any time, with incredible ease and expedition,
bring all their parts distinctly into view. To know,
therefore, the full value of tnas contrivance, we must
attentively consider the strict connexion that obtains
jbetween the several chesses of cur perceptions when
264 BU>-CAN's ELEMENTS
disposed in such a series. Every succeeding order
is formed out of those combinations that constitute
the rank next belovv it. And as in advancing from
one degree to another, we are always to proportion
the number of notices united, to the strength and ca-
pacity of the mind ; it is apparent, that by such a pro-
cedure, the ideas will be thoroughly ascertained in
every step, and however large and bulky, lie yet fair-
ly within our grasp. This obviously accounts for that
■wonderful clearness of apprehension, which we often
experience v/ithin ourselves, even in regard to the
most complicated conceptions. For though the mul-
titude of parts in many cases be great, I may say be-
yond belief, yet as they have been all previously
formed into separate classes, and the classes them-
selves distinctly settled in the understanding ; v/e
hnd it easy, by such a series of steps, to rise to any
idea, how complex soever, and, with a single glance
of thought, to embrace it in its full extent.
Sec. XVIII. — And communicating them by meann of
JDefiniiions,
But it is not enougli that we barely form ideas in
our own minds : we must also contrive a way to ren-
der them stable and permanent, that v/hen they dis-
appear upon calling oil' our attention, we m.ay knov/
how to retrieve them again with certainty. This is
befit done by v/ords and descriptions, v»diich serve not
only to subject them to their ov/n review, but also to
lay them open to the perceptions of others. And in-
deed as one of the main ends of reducing knowledge
into the form of a science is, the easy and advantag-
eous communication of truth ; it ought always to be
our first care, v/hen v/c set about unfolding our dis-
coveries, to exhibit the several conceptions to which
they relate, in a just and accurate series of deiini-
OF LOGIC. 265
tions. For till v/e have distinctly transferrecl our
ideas into the understandings of those to whom we
address oursv-dves, and taught their connexion with
the appropriated sounds, all cur reasonings will
evidently be without eiTect. If men comprehend
not the true import of our words, and are therefore
led by them to bring wrong- ideas into comparison,
they can never sure see connexions and lieJjitudes
that really subsist not. But if, on the contrary, the
terms we use, excite those very conceptions in others,
M'hich they denote in cur ovm minds ; then, as the
several relations pointed out will lie fairly open to
view, they must needs be discerned with grea.t readi-
ness and ease, and stamp the character of certainty
upon all our deductions.
Sec. XIX. — The names of simple Ideas co7istitute the
original and elementai^j terms of Language.
Thus we see that the method cf scknre begins with
unfolding our ideas, and commjinicatinp; them by
means of definitions. And here it is of great impor-
tance to observe, that there must be in all languages,
certain original and elementary names, whence our
descriptions take their first rise, and beyond which
we cannot trace the meaning and signification of
Gcunds. For since our very definitions are made up
of .words, if we suppose not such primitive and funda-
mental term^s, into v/hich they all resolve themselves,
and where they at last necessarily terminate, it is evi-
dent there vrould be no end of explaining. Now it is
peculiar to our simple ideas, that they cannot be origi-
nally excited by vrords, but must always make their
ilrst entrance into the understanding by the actual
operation of objects upon it. When, therefore, in a
series of definitions, we arrive at the names of these
ideas, 'tis plain we can nush our descriptions no far-
^K2
266 DUNCAN'S ELEMENTS
ther,biit are necessitated to suppose, that the percep-
tions themselves have already found admission into
the mind, if they have not, definitions avail nothing ;
nor can they any other way be impressed upon us,
than by betaking ourselves to the several objects in
which the power of producing; them resides. Hence
it appears, that the primary aitlcles of speech, into
which the v/hole of language may be ultimately re-
solved, are no other than the names of simple ideas.
These, v/e see, admit not definitions. It is by expe-
rience and observation, that we grow acquainted with
their meaning, and nirnish ourselves with the percep-
tions they serve to denote. For finding that those in
vvrhose society we live, make use' of certain articulate
sounds, to make the various impressions of objects,
YVQ too annex these sounds to the same impressions,
• and thus come to understand the import of their
^words. This way of knowledge takes place, in regard
to ail our simple ideas ; but in many of those that are
complex, as they are the mere creatures of the un-
derstanding;, and exist no where out of the mind,
there are, of course, no real objects without us, whence
they may be originally obtained. If, therefore, they
could not be comraunicaledby descriptions, we should
be left wholly without the means of transferring them
into the minds of others. But happily it so falls out,
that all complex concepdons v/liPitsoever may be dis-
tinctly exhibited in definitions. For as they are no
•more than ditferent combinations of simple ideas, if
these simple ideas have already got admission into
the understanding, and the names serving to express
them are knc^^vn ; it will be easy, by describing the
order, number, ^nd peculiar connexion of the notices
comhincd, to raise in the mind of another the complex
nciicn resultlncr from them.
or LOGIC, 267
Sec. XX. — d Knoiv ledge of these previously supfiGsed
in handling any Subject scientifically.
Since then it is by simple ideas and their names,
that Ave unfold all the other conceptions of the mind ;
it manifestly-' follows, that in liandling any subject,
icieniifcallv. v.e must alv/ays suppose those to vvhoni
we address ourselves, previously iurnisbed by e>iperi-
ence with these f.rct principles and eiements of
knowledge. Nor is this by any means an unreason-
able /?osr'zi/a?z^77i : because the simple ideas that relate
to the sciences, being fev/ in num.ber, and coming
Aerv often in our way, it is hardly possible we should
be unacquainted with them, or not have frequently
heard their names in converse with others. What
principally demands our care is, to apply those names
aright and according to the strict use and propriety
of the language in Avhich v/e vrrite. 'Tis seldom ai-
IcAvible to change the signitication of words, especial-
ly those by which we denote sim.ple ideas. If, hov>'-
ever, such a liberty should at any time be found ne-
cessary,, we may still make ourselves undersiocd, by
mentioning the idea under its common name, and
si5:nifying its- connexion with the newly appropriated
sound. Indeed it sometimes happens, that nev/ and
unusual ideas of rhis kind are to be taken under con-
sideration, which we must therefore express by
terms of our own invention. In this case^, as the
ideas themselves cannot be laid open by dennitions,
we refer to the several objects whence they may_ be
obtained ; which though it excites not the perceptions
immediately, yet sufficiently ansAvers our purpose, by-
putting men in a way of being furnished Avith them
at pleasure.
Sec. XXI. — The order and connexion of cur Def rations.
This foundation being laid, the communication of
our complex conceptions by definitions becomes both
268 DUNCAN'S ELEMENTS
easy and certain. For since the ideas themselves are
formed into different orders, and these orders arise
conlinuajly one out of another ; nothing more is re-
quivtd on our part, than to observe a like method and
gradation in our descriptions. As, therefore, the first
order of orir compound nolions is formed immediate-^
h from, simple ideas ; so the term^s appropriated to
this order must be denned by the names of these ideas.
Arid as the second and all the succeeding orders arise
continually out of those combinations thatconslitiie the
clasr^s next belovr them, so the definitions corres-
ponding to these different orders gradually take in
the terms by which the several inferior divisions are
regularly and successively expressed. In such a se-
ries of descriptions, it is evident, at first sight, that
nothing can be obscure and unintelligible. For as it
begins v/ith the names of simple ideas, v/hose mean-
ing is^ supposed to be known — and as in every order
of definitions, such terms only occur, as have been
previously explained in the preceding distributions
—by advancing regularly from one to another, v\-e
gradually furnish ourselves with whatever is necessa-
jy towards a distinct conception of all tliat is laid be-
fore us. Nor is ii a small advantage attending this
disposition, that the several ideai d-jscribed are here-
by excited in the understanding, in the very order and
manner in w!:ic}i they are framed by a mind advanc-
ing uniformly fi-om simple to the most complicated
iiotions. Hence v\^e see disti.ictly the various de-
})cnde]Ke of things, and being put into that very
traui cf thinking which leads directiy to science cUid
certamt.y, are drav/n insensibly to interest ourselves in
the puriiuit ; insomucii, t iiat while in fact we do no more
than fojlovv a guide and conductor, v/e can yet hardly
forbear fancying ourselves engaged in the actual exer-
ts, se of deducing one p?.rt of knovrledge from ancther.
OF LOGIC. 269
Sec. XXII. — Of the immediate and iritidiive P^elations
bchvesn our Ideas.
When we have thus fixed and ascertair.ed our ideiis,,
and distinctly exhibited them in definitions, we then
enter upon the important task of tracing tlieir several
Iiiibitudes and relations. In order to this, we setabout.
ccmparing- them among themselves, and viewing them
in all the variety of lights, by which we can hope to
arrive at a discovery of their mutual agreement or dis-
agreement. Aiid here it happens, that some relations
fbrwajcUy offer themselves to the notice of the under-
standing, and become the necessary objects of percep-
tion, upon the very first application of our ideas one
to another. Tliose are, therefore^ immediately own-
ed, and constitute oiw primary and nr/t/zV/ve judgments,
being attended with the highest degree of evidence,
and producing absolute certainty in the mind. ^ But
in many cases, the connexion or repugnance between
our ideas, even vrhen true and real, comes not yet
within our immediate viev^^, but requires search and
examination to discover, it. On this occasion, v/e have
recourse to intermediate notices, and if by means of
tliem we can muster up a train of evident and knov;ii
trutlis, which, disposed in a regular series of argu-
mentation, lead at last to a conclusion expressing the
relations we are in quest of, the proof thence arising
is called demonstraiio?i. Now as the conviction at-
tending demonstraticn^ is no less necessary and una-
voidable than that which proceeds from intuition ; it
evidently follows, that whether the relations betv/een
our ideas are immedieiteiy discerned by the mind, or
whether they are ti'aced by means of intervening per-
ceptions, in either case we arrive at science and cer-
tauity. 1 his, hov/ever, is particularly to be observed,
that the more remote and distant respects, being de-
270 DUNCAN'S ELEMENTS
duced from such as are ob\-ious and self-evident, the
propositions expressing these last demand our first
Dotice, and ought to be previously established, before
we enter upon higher investigations. Vslien, there-
fore, in the mttkod of science^ we have fiiiished the bu-
sh:!ess of definitions; it must be cur next care, dis-
tinctly to uj-jfold in propositions, those immediate and
intuitive relations, which are necessarily seen and
ov/ned by the mind, upon the very first compaiingof
our ideas one with another. These propositions have
obtained the name of frst jirincihleh^ because; occur-
y\\\^ first in the order of knov/ledge, and being mani-
fest of themselves, they suppose not any p.rior truths
in the mind, whence they may be evidenced and ex-
plained. It is not needful to enlarge here upon the
necessity of circumspection and care, in setthng these
primitive and fundamental perceptions. For since
the v/hole superstructure of our Imowledge rests ul-
limately upon them, it is evident at first sight, that ?w
nilstake in this case must at once overturn and anni-
hilate ail our future reasonings. But having already
explained the nature of these propositions in the sec-
ond book, unfolded the notion of self-evidence, and
taught the manner of distinguisliing between the
truths of this class, and those that are demonstrable \
v/e shall, for tlie present, v/ave any farther considera-
tion of this subject, referring the reader to what is
tliere advanced, if he desires fuller information.
Sec. XXIIL— C/ the ahplication of Self-evident truths
in deiJio:istrating such as are remote end dist(z?ir.
The first and more immediate relations of our ideas
being thus pointed out, our next business is to inves-
tigate such as are remote and distant. And here it
is that vve have occasion for intermediate notices, and
a skilful application of intuit ve truths. But though.
OF LOGIC. 27-1
self-evident propositions be the ultiir. ate fonndation of
our reasoning, ^ve are not, on that account, to imagine,
that the art of improving knov/ieclge lies in assernb-
ling, at random, a large and comprehensive stock of
these. Even general /trlncifdes^ considered by them-
seU-es, avail but little to'vards the investigation of
truth. They are, indeed, useful as media of certaintv,
by preserving the evidence of our reasonings distinct,
>vhich never fail to convince, if, being pursued to
their so'irce, they are found to resolve themselves in-
to, and ultimately terminate in these principles. But
wh.en we set a.bout the increase and enlargement of
Lciencc, i-xv other helps are required. For li^co, the
vvhoie secret consists, in devising and singling v,\\t
such intermediate ideas, as, being compared v/ith
those others whose relations we enquire after, may
furnish out a train of obvicus and kno^.v'n truths, serv-
ing distinctly to investigate the said relations. Euclid,
in the first bock of the elements, has dem.onstrated,
that the three inward angles cf a triangle taken togeth-
er^ are equal to tni'o right angles. The reasoning, by
v/hich he establishes that proposition, resolves itself
into this general principle : things equal to one and the
same things are equal to one ancther. Will any one,
however, pretend to say, that a bare consideration of
the principle itself led him to that discovery ? The
merest novice in mathematics would, upon this sup-
position, be equally qualified for the business of inven-
tioii, v/ith one that had made the greatest progress ;
i.'iasmuch as these general principles of the science
are commonly alii-ie knov/n to both. But the truth of
it is, Euclid, having found out angles, to which the
three angles of a triangle, and tv/o right angles, being
compared, were found severally equal ; thereby as-
certained the proposition in question, by showing it
to teririinate in the above axiom, though perhaps the
272 DUNCAN'S ELEMENTS
axiom itself was never once thought of, during the
whole course of the investigation.
Sec. XXIV. — Reasonings though resolvable i7ito gener-
al truths^ rests immediately ujion fiarticidar self-
evident propositions.
And here it may not be improper to observe, that
though it be usual in reasoning, when we arrive at
any particula.r self-evident proposition, to refer to the
general axiom under wliich it is comprehended : yet
is not this done out of absolute necessity, or for the
sake of any additional confirmation. AH intuitive
truths, whether general or particular, star.ding upon
V\Q same foundation of immediate perception, are ne-
cessarily embraced for their own sake, and require
no mutual illustration one from another. When,
therefore, v/c have found, that the three angles of
a triangle, and two right angles, are severally equal
to the angles formed by one right line standing upon
another, we thence immediately discern their equali-
ty between themselves, independent of the general
axiom into which thi^ truth may be resolved. Nor do
we in reality refer to that a>riom, by way of evidence
and proof ; but merely to show the coincidence of the
example under notice, with a previously-established
general principle. The same thing happens in all
other demonstrations whatsoever, vvhich, terminating
thus in particular self-evident truths, are therefore of
themselves sufficient to certainty, and acquire not any
nev/ force by being ultimately referred to general
maxims. This I mention here, to obviate a common
prejudice, whence many are led to imagine, that
particular intuitive propositions derive their evidence
from those that are general, as being necessarily in-
cluded in them. But since they both stand upon the
same foundation of certainty, and are admitted in con-
OF LOGIC, 273
sequence of immediate perception) they have there-
fore an equal claim to self-eviderxe, and cannot be
made plainer by any mutual appeal.
Sec. XXV. Particular Sclf-z-vident firopodtirms so
called hej'e, hi opjiosidon to genei'al Jirmciplss,
As, ho'.vever, it is usual in the method of science to
lay down certain general principles by way of foun-
dation for cur future reasonings ; some will perhaps
object, that this seems to be a needless precaution,
since demonstrations may subsist without them, and
comimonly terminate in particular self-evident truths,
peculiarly connected with the subject under consider-
ation. In order, therefore, to give a distinct idea of
the true design of this previous step, v/c shall begin
with observing, that by the particular propositions in
v.-hich demonstrations terminate, must not be under-
stood such as are so, according to the strict definition
of the word, or in opposition to universals ; but only
confined and limited truths, when compared with
others that are more general. Thus the proposition,
ci^cles^ equal to one and the same circle ^ are equal bc-
tKveen themsebjes^ is, in strictness and propriety of
speech, universal, because the subject is taken in its
full extent, and the predicate agrees to ail the indi-
viduals comprehended under it. We here, notvvith-
standing, consider it as only a particular truth ; be-
cause it is of a very limited nature, when compared
with the general axiom mentioned above : things c-
qiialto one and the same things are equal to one another.
For this not only extends to all the var:~c»us species of
figures, but takes in every object without exception,
that comes under the denomination of quantity.
L2
274 DUNCANT's ELEMENTS
Sec. XXVI. — General Prlncifihs serve^Jirst, to Coii'
tract the bottom of our Reasoning .
This point settled, it vvill easily appear, that the
iiie'Lhod of premisiriC; general principles in the scien-
ces answers these two great and valuable purposes.
Fir fit ^ to contract the bottom of our reasoning, and
bring it within such bounds as are sufficiently accom-
ir.cdated to the capacity of the mind. For demon-
strations being carried on by means of intermediate
ideas, which must always have some peculiar connex-
ion 'with the matter in" hand, the particular self-evi-
dent propositions in which they terminate, are almost
as various as the subjects to Y»'hich they relate. Thus
in investigating the equality of different objects, wheth-
er angles, triangles, circles, squares. Sec. the intuitive
truths, on which the proofs rest, aivrays regard the
particular species, and may be therefore multiplied,
iiz infinitum^ as |well as the species themselves. But
now it is remarkable, that ail these several truths, nu-
merous as they may appear, are yet reducible to this
one general principle already mentioned : things equal
to one and the same things are equal to one another. The
same observation will be found to hold in other parts
of human knowledge : insomuch th^it though the par-
ticular truths, on which we bottom our reasonings, are
really innumerable ; yet m^ay they be all, v, ithout ex-
ception, resolved into a very fev/ general maxims, and
thereby brought readily within the compass of the un-
derstanding. When, therefore, we begin v.ith pre-
mising these general truths, and as we advance in
science, take care universally to resolve our demon-
strations into them ; this must needs add a wonderful
cleaiTiess and perspicuity to our reasonings, and by
establishing them upon a foundation previously ad-
mitted, and of whose strength and firmness we are
OF LOGIC. 275
abiiRcIantly satisfied, give them that irresistable force
and inliuence, Vvhich serves to produce absolute cer-
tainty. Nor can we possibly imagine anv thing more
elegant and beautiful, than thus to beheld knowied;'^e
rising from a firm and fathomable root, bearing its
Iiead aloft, and spreading forth into innumerable
branches of science ; vrhicb, though variouslv impli-
cated and entangled^ and stretching to a vast extent,
yet by their union in one common stock, derive
thence so sure and stable a s,upport, that all the as- .
saults of cavil ani scepticism are net able to destroy
or loosen their connexion.
Sec. XJ,Vll.—-Second/y, to ascertain the Justness cfit.
xolth more Ease, and less Hazard cf Miscarriage.
But, secondly^ another purpose served by general
prmciples is, that they enable us with less fatigue and
labour and less hazard of miscarriage, to satisfy our-
selves as to the justness of those reasonings by whicli
science is establiohed. For since dem.onstrations,
when pursued to their source, terminate ahvays in
particular intuitive truths, which are therefore the ul-
timate foundation of certainty ; it greatly improves us,
to beware, that we receive not any propositions under
this name, until we have distinctly st;ttled them in
our own minds, and attained a full and clear percep-
tion of that self-evidence, on account of which they
are admitted without proof. But now these proposi-
tions being m.any in numb^sr, and diiTering according
to the nature of the subject about vrhich our researches
are em.ployed ; it must greatly perplex and retard our
reasonings, were v/e to check ourselves every time
they occur, in order to examine them by the rules of
first principles. Nor is it a m.atter of slight consider-
ation, that in the heat and hurry of demonstrating,
wniie the mind is advancing eagerly irom one discov-
276 DUNXAN's ELEMENTS
ery to another, v/e should be often tempted to pass
them over hastily, and without that attention their
importance requires ; wliich -must expose us to many
errors and mistakes. These inccnvcniences are cf-
f jctually prevented by the method of premising gen-
eral truths: because upon referring particular propo-
sitions to them, as the connexion is obvious at first
'jitrht, and cannot possibly escape our notice, the evi-
deiice is discerned to be the very same v.ith that of
t"::e principles to which they belong. And thus by a
bare reference, without the trouble of particular ex-
aminatior:S, the grounds of reasoning are ascertained,
and our demonstrations found ultimately to rest on
znaxims previously established.
Sec. XXVIII.-— Q/'--''^ vmnner cf linking firofiositions
^ iotscther^ in order to the fanning cfkgitiinatt demon-
it t rati oyis.
Having explained the use of general principles,
shown them to be the great media of certainty, and
found, that in order to enlarge the bounds of science,
we must have recourse to intermediate ideas, as by
means of them, w^e are furnished with the several pre-
vious truths, of which reasoning consists ; it nov/ re-
mains, that.v/e enquire in what m.anner these truths
5 re to be disposed and linked together, towards the
rV^'ining of just and legitimate dcinonstruti-:.7is. We
i^ave seen already, in tlie preceding book, that syllo-
fei&ms^ drawn up accordinu; to the rules there estab-
lished, lead to a certain and infallible conclusion, if
therefore endent and allowed truths are disposed in
a Syllogistic order^ so as to eiier a regular conclusion,
that conclusion, is n.ecessarily true ui»d valid. Ar^d
si-ce in every geiimne syllogism, if the premises are
true, the conclusion must needs be true ; it nianiiest-
;y fcllov/S; that the conclusion flireddy g-ained, bemg
OF LOGIC. 277
rjow a known and established truth, may be admitted
as one of the premises of any succeeding syllc^-rism,
and thereby contribute tovrards the obtaining a new
conckision. In this manner may syllogisms follov/
one another in train, and lead to a successive discov-
ery of truth ; care being always taken, that the prem-
ises, in every step, are either self-evident propositions,.-
or conclusions previously established. And indeed
th.e Vv hole art of demonstratiiig lies in this due and or-
derly combination of our syllogisms. For as by this
means all the several premises m.ade use of are man-
ifestly true, all the several conclusions must be so too,
and consequently the very last conclusion of the se-
ries, which is therefore said to be demonstrated. The
same order is to be observed in the disposition of the
demonstrations themselves. That is, those proposi-
tions are ahvays first to be demonstrated, which fur-
nish principles of reasoning in others ; it being upon
the certainty of the principles made use of, that the
certainty of the truths deduced from tliem depends.
And since even the different branches and divisions of
scieiice have a near connexion among thcm.seives, in-
somuch that the knov/ledge of one is often presup-
posed in another ; great care must be taken to adjust
tne several parts with an eye to this dependence, that
those may always come first in order, whence the
{iosculata of demonstration in others are borrowed.
Sec. XXIX. — Why the method h^re exfikdned la called
tkj method cf science.
In this v/ay of putting together our thoughts, it is
evident at first sight-, that however far v^^e carry cur re-
searches, science and certainty T/ili still attend us.
But what is particularly elegant and happy in the
method now explained, we hereby see knowledge ris-
ing out of its firbt elements, and discern dlscinctiy ho^F
278 DUNCAN'3 ELEMENTS, tzc.
those elements are combined and interwoven, in ordes
to the erecting a goodly structure of truth. Exfic
rience furnishes us with simple ideas and their names,
which are ih^jirvnui^y materials of thinking and com-
munication. Z',y??2zV/o72s teach how to unite and bind
these ideas together, so as to form them into com-piex
notions of various orders and degres. The general
pHncihlcs premised in science exhibit to the under-
standing sucji intuitive and fundamental truths, as
expi-ess the immedfete relations between our ideas,
and constitute the ukiniate groimd of certainty. De-
7nonai rations link known and established truths togeth-
er in such manner, that they necessarily lead to oth-
ers vrhich are unknown and remote. In fxne, the du-
ly adjusting the sev^erai branches of science, and the
^lemonstrations in every branch, lays knowledge sa
oper. to the mind, that we see the paits of it grov.ing
one out of another, and embrace them with full con-
viction and assurance. Thus are we gradually led
from simple ideas, through all the windings and
labyrmths of truth, until w^e at length reach .'lie high-
est and most exalted discoveries of human reason. It
is true, the method here laid down hath hitherto been
observed strictly only among mathematicians ; and
is therefore by many thought to be peculiar to num-
ber and magriitude. But it appears evidently from
what vre have said above, that it may be equally ap-
plied in all sucii other parts of knowiedge as rega.rd
tiie abstract ideas of the mind, and the relations sub-
sisting between them. And since, wherever it is ap-
plied, it necessarily begets science and ceriai?2ty, we
• have heixe chosen to denominate it the method of
tcicTicc. the better to intimate iis true n^^.ture and ex-
tent. * . •
F I N I S.
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